So, I'm pretty sure most of what has been suggested to me thus far for this is probably the correct answer (that being: rebuild carb), but I figured I'd pose the question here just to be sure.
Earlier this year, I noticed that the car doesn't seem to like heavy throttle anymore (that said, this has happened on a few occasions of light throttle applications - I will detail below). If you get on it, it just doesn't go anywhere for a good few seconds - it's hard to describe exactly what it sounds/feels like, but it's almost like a rough/grating sound, mild sputtering (without actually sputtering). It just sounds "rough", and it just sits there not really accelerating, until it suddenly smooths out and pulls way harder (relative, given you were just not going anywhere the second before).
I'm sure not coincidentally, this seems to have also come at the same time as the vehicle starting to a rather low idle. The car starts (right up if it's been run in the last couple days, after the usual long cranking if it's been more than a few days - car has always been that way, probably the bowls draining or something) and idles at roughly 500 RPM, so you have to give it a rev or two to keep it from stalling. Those revs sound very "broken up". After a few seconds, it goes up to ~700 RPM where it should be, and sits there just fine.
Driving the car like a normal human being seems to be mostly fine, but as I've mentioned earlier in the post, sometimes you can notice it. One time that stands out in my mind was really the first instance where I noticed this all happening, leaving my spot after a car show back in June. Car started up right away, since I had driven it there in the morning, and then I went to pull out of the spot, but I looked like a total rookie with the car hopping up and down like it was trying to stall (4-speed car)...but I was driving it like I normally would, it's just that the gas I was giving it didn't seem to be doing anything at all. Then suddenly, that "smooth out" hit and the car took off, since now my foot was in it far more than normal, trying to get it to go.
I'm thinking maybe something to do with the accelerator pump, but I've really got no idea.
Made sense to post here before I go rebuilding the carb, in the event that maybe this is something else. For what it's worth, it did not do this at all last year, nor did I notice it the few times I started the car and let it run up to temp over the winter.