On many mornings there is a cart selling tortas de lechon on the side street 1 block south of Constituentes off 307 on the west side. (Around the corner just south of Covi). The other great lechon cart is under the blue tarp at 30th ave and 30th st. Whole suckling pigs last just a few hours at both locations.
The food at Alux on west Juarez is not remarkable, but the cave is one of the most incredible natural attractions in the Yucatan and well worth a drink and an appetizer. Nearly every other cave (cenote) in the region is at a lower elevation and was flooded long ago by salt and sweet water, and makes for world class cave diving. Sometimes I enjoy a drink underground without a regulator.

I became familiar with kecap manis when I learned it was the secret ingredient in a delicious chicken lunch I enjoyed on a catamaran in St. Maartin. I bought a dozen bottles to take home, 2 broke in my dive bag. It's a lot better on baked chicken thighs, served hot or cold, than on my regulator!
I still call it chicken Gabrielle, named after the catamaran.
Kecap manis is a strong flavor. It and a bit of orange juice concentrate and some chicken parts makes for good poultry.

Grocery - I prefer Chedraui. San Francisco is small ( it was the first ), the others have equivalent items but Chedraui is easier in and out. They can have surprisingly good fish - fresh boquinette for example - and nice head-on shrimp, which comes from Veracruz. It varies daily.
Dac's is the largest / best green grocer in the area, by far, owned by a prominent local family. They have a nice selection of dried chilies and spices, and a food service area with treats and liquados.
There aren't any farmers markets. Produce is trucked in daily mostly from outside of the Yucatan. Dac's and Marsan have large sacks of oranges for great juice. The valencias from Veracruz are worth the extra 2 bucks.
The fish markets you mention in Puerto Morelos must be fairly new (there is a lot of new development there in what has been a sleepy town forever). Maybe they have conch, which feed in turtle grass flats in the area. Conch in PDC is not so common. There is plenty in Cozumel. Fish for the Cancun market comes mostly from a fleet in Isla Holbox.
Pizza - there is a Domino's ( w/ local delivery) on 10th ave. between 6-8 sts, and a few by - the-slice bodegas in that area on 10th ave, and on 10th st a block either side of 10th ave. Dr. Taco, (killer shrimp tacos) and the taco bodegas in that block would be fun for the tykes.
Panaderia del Carmen has nice breakfast pastries, and cornbread and bollo rolls for your Supercarne arrachera take-out. See how it all knits together? Buen provecho!

Good burgers at Cherry Cricket and Bull & Bush. Both do a mean blue cheese and bacon burger or smothered with green, as you like it. Cricket has a very large bottled beer selection; B&B brews on premises and has growlers and a Dixieland band on Sunday nights. Under 10 bucks well spent.

Cross streets in Polanco on Masaryk are alphabetical west to east, all named for writers. From Aristotoles to at least ( Edgar Alan ) Poe is an easy and pleasant walk. Pujol is at Horacio. When I lived on Campos Eliseos I walked everywhere in Polanco. It is quite compact and has a large orthodox jewish community on its west side.

My imagery on this one is somewhere between a sword swallower and a seal catching a fish. I would like to watch.

In my experience jarred wasabi powder "heat" has a half-life of about a year in my pantry, less for the jar I keep in my car. Any "heat" ingredient should be tested / tasted before adding fixed quantities of it to a recipe, especially chilies. Adjustments are often necessary. Your wasabi powder probably became flavorless some time ago.

Food court operating expenses, including rent and common area maintenance, are pro-rated to food service tenants in their occupancy cost, which is incredibly high. Bringing one's own food to a food court is akin to bringing one's own candy to a movie theater. Easy to rationalize, but as the defensive tone of replies here underscores, the practice doesn't win any merit badges. When the amenity is abused, usually by loitering teens, it is correctly a tenant-landlord matter and limitations to 'invited guest' legal status can be put in place.

All purpose grocery - Chedraui , 307 S. of Juarez, east side, often has most of what you will need. Nearby on S. 1st st, Marsan at 40th ave for fruit and veggies, Supercarne at 25th ave. for arrachera take out, with roasted potatoes and onions. Very good, you can buy uncooked meat but they do it better. A few places on 2nd st between 20 & 40 aves roast chickens daily, follow the smoke and your nose around noon.
The best fish market is Oceana, 34th st at 35 ave. The best produce in that area is at Dac's, on 30th ave. a block n. of Constituentes. A couple of the kids can get a good smoothie (liquado ) there, also.
The bakery at Chedraui is large and pretty good. You can get into and out of Chedraui quickly without getting snarled in PDC traffic. Puerto Morelos is way too small to have what you need.

I suggest Baci for Friday night, in Turtle Cove. It's an easy ride west on the bight road if you are staying in the Grace Bay area. And a good compromise between Da Conch Shack and Anacaona - they are the extremes!

And "zuppa di clams" sounds sexier than "clam soup".

Playa del Carmen is an anomaly in that english is the common language, over 50%, the remainder is spanish followed by italian and german. Employment restrictions dictate that a high % of employees be native, but numerous restos use their "wild card" to hire attractive english speaking shills to hustle business from the endless street strollers. Which is OK.
Concerning mayan fare, the Yucatec mayans were screwed out of interior grazing and farmable land a few centuries ago, and were relegated to the inferior "beachfront" land that is too salty and sandy to support either. They became fishermen, now numbering just a few hundred.
Since 1990 the spanish-mexicans with political control have appropriated much of the now-valuable beachfront back from the mayans, to enable the countless all-inclusives along the Mexican riviera. The ancillary horror stories of how that came about are off topic.
Back on topic, I don't think there is a range of truly authentic mayan fare that could support a mid to high end resto, without the addition of 'fusions' and 'interpretations', so I personally don't object to the menu at Yaxche. And importantly, no one else is trying, so it's the best that's in the area.
Also, there is not a problem bringing one's special wines to a local resto that does not feature wine. You should not expect stemware, and bring a corkscrew, too. I have friends in Texas who go to Playa a few times each year, and they travel with a wine chest the size of a coffin.

I'm familiar with the 6 on your list that are not in resorts. Unfortunately, "mayan inspired" and "fine wines" do not go hand in hand in the Yucatan. The best wine experiences wil be at Cocina 38 and Negrosal. Negrosal has a nice cellar with a tasting area under the glass floor in the dining room, they will give you a quick tour. It's nicely organized by country, and they have a few D'Yquems and Petrus' , but more as a gimmick, I expect. An occasional contributor here, wineman3, is the wine merchant to both. The sea bass in banana leaf at Negrosal is really good when they get it right, and the grilled octopus appetizer is consistently amazing. Cocina 38, in the "little Italy" part of town, has good fare and wine, but is not mayan (nor is Negrosal, but both feature LA/SA dishes).Either is a good spot for a long lazy dinner. La Choza in Cozumel, authentic as it is, would be better for a lunch. Wine selection is blanco or tinto, take your pick. Chairs there are not comfortable for a long stay. Yaxche is interesting. Portions are small so you will need to enjoy several courses to get your fill. Marginal wines; try something different like an after dinner Xtabentun. Yaxche is the only spot in the greater area that attempts mayan. Sometimes they are a little full of themselves, but it's a nice experience. Hechizo in Tulum is small and intimate, but again one is in and out fairly quickly, considering the drive, and there is no place to hide a wine cellar. But it has the passion and reverence you seek. Labna in Cancun is a mercantile machine, Playa folks tend to avoid Cancun.
El Sol and Pavo Real, both at La Maroma, I'm sure offer a long, lazy evening. It will be pricey, Maroma is rock star prices. When it first opened it was not accessible to non-guests, and has security tighter than Los Alamos. It is a large, elegant beautiful property. Buen provecho!

Somehow a famous scene in Casablanca with Humphrey Bogart and Ingrid Bergman would not have been the same if Rick had said to Ilsa "We'll always have McDonalds."

Wow! Beef, bacon, chorizo, cheese. Small wonder you didn't want to eat until the next day. And you were perhaps lucky to wake up the next day ;)

As it is said, a hot dog tastes best anywhere but home, but a chorizo dog - now that's a horse of a different color. Although with that metaphor I may have one too many animals in play.

Bacon in Mexico used to be great stuff - thick, smoky, crispy, very tasty. I can remember back to when I would order a side of tocino with huevos rancheros, and sometimes there would be no extra charge. Today Mexico is plagued with this faux deli- style processed crap everywhere one goes, that shouldn't even be called bacon. Times have changed.

Chorizo with onions and peppers can substitute on a chili dog, and is easy to make in small quantities.

I hope that a take-away by those reading this thread is to have a spare house and car key in several strategic locations, apart from a neighbor.
Check the date on your kitchen fire extinguisher. And watch the toaster oven vigilantly while in use. I had a flaming inferno making garlic bread in one, and quickly put it out. It could have been a bad one had I not been there. And candles may be a nice seasonal or romantic touch, but they are trouble in the making.

Queso fundido with chorizo is an option. Cut away casing, fry chorizo until nuggets are almost crispy. Different brands and qualities of chorizo will yield different amounts of red fat. Save the fat to mix in with black beans or frijoles charros. Add chorizo to melted quesadilla cheese or any queso fundido recipe. Serve like a fondue on warm flour tortillas.

As I said. Two backstraps = two tenderloins per deer. I carve them out all the time.

A backstrap is a tenderloin, period. Cylindrical, about a foot long, nothing but lean. There is perilously little moisture to preserve, and no fat. Think of a cross section as an archery target with 3 concentric circles. To cook the center through, you will toast the outer ring, which is 55% of your meat.
A good argument for slicing.

During the post-hunt card games at the camp in PA, we slice the backstraps into medallions and flash fry them, 30 seconds per side, in a tad of oil, Worchestershire, and cracked pepper, and keep serving them up as appetizers. We call them "speedies".
Backstraps are so lean, be careful if you cook it whole so as not to dry it out.

pomodoro salad
sarsuela de peix (pretty much a cioppino with saffron) with shrimp, clams, mussels, and scallops in wine & fish broth, over whole grain linguini, with plenty of sauteed cebolla and ajo and colorful sweet peppers.
key lime pie

And if it hits the ground running, let it go.

No answer yet to the question of price, but last season's Vermont grade B runs about $18US/ quart, which is 3.9BP per 330ml.

That's what I do also, and then I sieve out the very fine particulate.
bonus points: it works during a power outage.

Have you tried a lobster burrito at Waruguma's? Victoria House is always reliable and very pleasant with a group. You might check the "new in San Pedro Belize?" thread on the Caribbean board for more posts about Ambergris and Caye Caulker while you are still in the area. I have cleared customs sailing from Isla Mujeres, I'm curious where you cleared customs entering Belize? Corozal maybe, or does Ambergris have a customs office now? Did you do any fishing or spearing in the Chinchorro banks?

I'll sometimes scarf down a Whopper and beat a hasty retreat. But linger over a beer? Unlikely. Lighting is at interrogation level, seating comfort is at Salem witch dunking level. I like a frozen mug or pilsner glass for beer, unlikely at BK. Oh, and a view of what?
These concept stores are in heavy tourist areas, and tourist standards are, shall we say, tolerant.
Fast forward to the next hypothetical test concept: the BK wine list.
"From that dollar menu, gimme a paper cup of that April vintage red ..."

Years ago on my way to the Poas volcano in Costa Rica I happened upon a resto and a bowl of black bean soup with a poached egg that was cosmic. The sweet memory ricocheted in my cranium for a couple years. My next trip to CR was designed around another bowl of soup.
Sassifying!