Hesitation

It could be in the distributor, but it has nothing to do with points as long as they're set properly- is it a single or dual-point?). If the advance mechanism is sticking, it could be as simple as lubing up the plates and pivots, I wouldn't be surprised if it's never been done for 50+ years). Could also be a dried out accelerator pump, or a misadjusted kickdown linkage, or a myriad of other things. DON'T just start throwing parts at it. You're not going to throw fuel injection on it if some other putz tells you that carbs are garbage and that's your problem, are you?