fredb2548, you are my new hero on Chowhound.
I think I'm pretty good with words, but I could not improve on your above statements about taste and locality. Thank you for proving that internet discourse isn't necessarily a lost cause. I hope other folks around here will read your words and take them to heart.
Country Barbecue on 68 and on Wendover are both still open. There was at least one other location in south HP, maybe it is the one that closed. That said, I can't recommend the chopped BBQ from Country. I've had it several times, and it has been dry each time. No amount of sauce can cover it up. The sliced might be better, I don't know. I do like their fried tenderloin -- it is especially tasty in the morning on a biscuit.
My experience with Carter Brothers chopped BBQ is, if anything, even less inspiring. I can't recommend any alternatives here. Not a fan at all.
If you are determined to find chopped BBQ in HP, I would probably go with Kepley's. I've been there only once or twice, and while underwhelmed, I like it better than either Carter Brothers or Country Barbecue.
If you're willing to go for barbecued chicken instead of pork, Big Ed's Chicken Pit is the very definition of a hole in the wall, and might not be world class, but is a tastier option than chopped bbq from any of the HP places. (North Main St, across the street from Lowe's hardware store.)
You mentioned Stamey's, and if you want chopped BBQ, it is head and shoulders above anything I have ever had in HP. I don't know if it will fit in with your time constraints, but if you can make it work, it's the right choice. It is directly across the street from the Greensboro coliseum, and would be only a few minutes on I40 from GSO airport.
Just my opinion.