Don't know if you got your problems solved yet?

I'd check the vacuum advance cannister on the side of the distributor. It will have a rubber hose running up to the carburetor or just below it. Pull hose loose at carb, take off distributor cap. Suck on the carb end of the hose to draw a vacuum then plug it with the tip of your tongue, while watching points plate.

This application of vacuum should cause the points plate that points are mounted on to slowly turn - revolve. Holding vacuum with tip of tongue, plate should stay advanced, not slip back to retarded position. If there's no movement at all the vacuum advance cannister's diaphragm is ruptured or dried out or the lever coming out of cannister that hooks to bottom of points plate has come loose. Of course if the vacuum hose isn't hooked up then nothing's going to happen at all.

Under normal circumstances this vacuum is maximized when you step on the gas to accelerate and the points plate moves to advance the timing for more power. The closer to WOT [Wide Open Throttle] you go the more vacuum, hence the more advance. Some vacuum advance is needed anywhere above idle, especially under acceleration.

Just the vacuum cannister can be replaced, should still be available from parts stores. Also the vacuum hose has to be in good condition, not dried out, and tightly connected at both ends.

You can also start engine with distributor lock-down bolt loosened a bit, just loose enough that distributor will turn with some effort. With disto loosened start engine, slowly turn distributor with engine running. Vacuum advance should be on left side of distributor. Turn distibutor slowly counter-clockwise [advance] until engine misses slightly, then turn it back a few degrees clockwise. Try throttle to check for improvement. Pinging and missing indicates too much advance. You can turn-in this running timing improvement to a point that engine just quits pinging under load, then a hair bit more clockwise and retarded. That should be real close to correct timing. Don't test drive it with distributor lock-down bolt loose. Changing points gap can change timing slightly.

Also an engine can run sorta okay at idle but when you try to accelerate a vacuum leak can cause a missing, some real bad running. Carb needs a good gasket and phenolic insulator, no leaks.