Well I finally got the car to start up at any given moment now, no guessing. But now when I turn it off, it keeps going for about 10 seconds like I'm choking it to death instead of just shutting right off, and it's loud when it does so.
Sounds like you have the primary throttle plate open too far. Once the butterfly opens past a certain point, the idle circuit is removed from play and the booster venturi supplies all the gas. As draw still happens across the booster, enough fuel air mixture continues to enter the hot engine and dieseling occurs. Back the idle screw out a bit. If you had to turn the screw that far to get it to start reliably then there is an issue with the idle circuit and you should probably rebuild the carb.
Check the timing. TDC, pointing to #1, then with a light. When the engine is cold the fast idle cam will be rotated against the fast idle set screw to make the engine idle faster. After warming, the choke spring will rotate the fast idle cam out of the way and normal idle should be achieved. No need for warm idle to be faster if the choke and idle circuits are working correctly. Most starting issues can be traced to improper setup with the second biggest cause being improper choke operation or vacuum leak. And just because it was rebuilt doesn't mean it was done right. Stay away from assumptions. Did you get a rebuilt carb, or did you rebuild it yourself or have someone do it for you? The key is to dip the carb to clean all the crud out of it. Complete disassembly, thorough cleaning, reassembly, proper setup. Check for vacuum leaks as well - a little starter fluid at the gaskets to see if the engine picks up or not. Is this an Autolite 2V?
I had a similar problem with mine, and the run-on was traced back to my MSD ignition. The only difference with my problem was the fact the engine continued to run for several minutes, as if I never attempted to shut if off. Instead of messing with anything in the engine bay, I pulled the manual choke which eventually starved it.
I looked in my MSD manual, and read that a diode may be needed to alleviate this very problem on some setups. After this was installed, run-on hasn't been a problem.
So in case you're running an aftermarket ignition, you could be experiencing the same problem I had.
I'm about to order the Ignitor setup for it, but as for now it's the stock stuff. The ignition seems to work now, but I took it to a guy today who charged my 25 bucks to correct the timing and tell me that the new alternator I installed yesterday isn't charging my battery. It has power, but something about a switch post....I dunno. All I know is that I'm starting to go broke just to get the thing running, which I was promised would be the state of things when I bought it.