Here are a couple more pieces of info that might help pin this trouble down.
First, I didn't mention before that the carb is a Rochester B. I know, I know, but that's what was in there when I got the truck

.
Second, I recently installed Fenton headers. The problem I described at the top of this thread predates the headers, but it got worse when I put them in, which is why I'm working on it now. I've seen vacuum leak suggested, but would that cause a problem only when I push the pedal too fast and leave the engine running as smoothly as ever otherwise?
Third, in another thread I saw that headers often require a richer mixture than stock exhaust, so I tried adjusting the mix. That made the engine 90% better, but I had to adjust it 2-3 turns out before it made a difference, and now I think I'm running too rich. And it still has a bit of hesitation on acceleration. Also, I notice it mostly in second gear. It barely does it at all in first. Is that significant?
-Jon