I'm going to ask just to be nosey i guess. It acts like its just missing out something bad right? You have check and rechecked plugs wires timming the best you can while its missing right? Its not back firing anymore not poping any more?
Now not tellong you what to do but just telling you what i did when my 350 was acting like that. It was missing something bad. Id put it in gear and the whole truck would act like it was trying to buck me out.

i was running a quadra jet. I could not fine a thing wrong with anything ( plugs, plug wires, timming didnt help) I called my cousin who is a machanic by trade he told me to find a differant carb and try it. I talked to a buddy in town borrowed a edelbrock 600 he had on a shelf. Slaped that baby on hooked every thing up. Turn the key she ran like a champ. Gave my friend $100 for it and have not had any trouble since.
Now the other day i got stupid a little and when i put carb on i didnt adjust my kick down for the th350 tranny and i got the kick down stuck and it would idle ok but put it in gear and hold on it would shake rattle and roll. I adjusted the kick down right and had no problems at all runs great kick down work etc...
So i guess even though you have had the carb checked and it may be new. You may have a piece of somthing stuck in a jet or something. Slap a differant one on and try it. Im just saying you'd be surprised.