base timing keeps advancing by itself...

OK it followed using another distributor, I am assuming a points one sice all the electronics are in a petronix. Really a weird one Cooling down sure seems to be a electrical issue. What exactly is in your ignition ststem from the ignition power all the way?

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I think "another distributor" was used to replace/repair some parts on the suspect one? That's how I understood it. Still, it reinforces an electrical issue.

I still suspect there's not a real problem and the idle is just hanging higher when 'hot' (versus 'warm') which keeps more advance in it. Insufficient cruise advance can cause the chambers/plugs/valves to run much hotter which will also raise the idle speed after a drive. Higher idle will pull advance in and keep the idle high.

Super stout springs would help so that it can advance at slightly higher rpm but ensure no advance at idle up to say 1800+ rpm.

Or increase the all-in timing (I think he said it was 24? But it's unclear), or richen the idle mix a bit - but those won't directly confirm or disconfirm what I'm suggesting.