Since it runs fine with the choke cold/closed, but won't idle after the choke is warm/open, I'd say something in the carb is the problem. May just need to screw in the throttle adjustment screw enuff to keep the engine running when warm.

Might also help to make minor adjustments to the idle air screws, to see if they make any change in idle speed.

Sometimes a Q-jet can get gunked up so that the idle circuit does not work properly. That would require a clean-out/rebuild.

I'd also check the initial timing, at idle. I use to run mine at aprox 12-13°.

"...Maybe the weights in the HEI are sticking?"

At idle, the weights should be pulled all the way in, by the springs.

A malfunctioning vacuum advance can cause idle problems. It should also have a constant, adequate vacuum supply.