Improving acceleration using 2bbl Carburetor?

I'll do my best.
I’ve been having an issue for the past month or two where it takes a few tries to start it. If I’ve just driven it, stopped to run an errand, and then get back in, it starts up in a second or two. But when I’m starting it for the first time that day it takes two or three tries to get it cranked. If i drove jt around and then don’t drive it for a few hours (still warm but not hot) it takes several tries.
That's not unusual depending on how you prime it (pump thr throttle) and the choke setting. On a '64 factory settings for idle and choke should provide pretty good starting in all conditions. But today's fuels have distilation curves that can make it starting a little more difficult after the fuel has been sitting in the bowl for a while.

I think this is an issue with the timing of the ignition. The distributor and starter were initially replaced back in November/December and had the timing set. Started and ran fine consistently then. The distributor gunked up and was replaced back in February, and the timing was set. It started and ran fine consistently. But now it doesn’t.

Is it a heat/humidity thing?
Yes the initial timing can make it easier or more difficult to start the car.
I am concerned that the distributor has been replaced and replaced twice.
I'm also concerned about what 'gunked up'.

I’ve read up on and watched videos on how points and condensers ignition works, how adjustments are made, but don’t totally understand it
Well you don't need to understand how they work to make the adjusments. Just follow the procedure.
Doing so may help you pick up on how they work. A lot of us learn like that. We can read about it, and we can work on the parts, but only when we do both are we able to understand what they do.

Would an HEI conversion help with cranking?
Pretty much the same answer I gave before about electronic ignitions in general.
IF the combustion conditions are such that a slightly higher voltage will initiate spark and if more current will build a better flame kernal so there's a good burn instead of a misfire or incomplete burn, THEN yes.
So in other words, if something is going in inside the cylinder that is making it difficult to initiate combustion, then a good HEI or similar setup may be able to overcome those conditions.

Note: at one point I had trouble cranking due to a bad alternator wire and it was draining the battery trying to crank that.
Not sure what you are describing.
A battery that doesn't get recharged will definately make it difficult to start.
Otherwise the alternator isn't involved in starting.