If you think of the heirloom tomatoes and lemon basil that you get from the farmers’ market as your precious babies, then consider wheeling them around in a stroller, like the Hook and Go, a rolling, foldable tripod thingy you hook your bags of produce onto. It can hold up to 70 pounds, and is the must-have accouterment at the Beverly Hills Farmers’ Market and the San Francisco Ferry Plaza Farmers Market. And having your hands free means you get to bring home a lot more fruits and veggies.
I'm sure it would work equally well with canvas bags. No need to use plastic!
My biggest concern is that you still have to use plastic bags for all your purchases. Seems like it is a lot more wasteful than other types of rolling carts.