Vacuum advance

at Idle, the engine will easily except 20/25/30/ sometimes even more degrees of timing, with the rpm climbing continuously, indicating that more and more power is being produced.
Yes. In Neutral!
With no load engines like lean burns. Even with slight to moderate load engines like lean burns.
Power goes up with rpm. So any time we increase rpm we increase power.
The way to compare power is to be at the same rpm, with two different spark leads.
Then load each to the point of stall.
The one that can turn the highest load has the timing that makes more torque and power.

At idle; you gotta dial the power back, else the engine will pull hard on the convertor, which becomes very annoying at every stoplight.
And I'm saying that's not what's happening. It's not that there is too much power. It's not that there is more torque produced by the engine with more spark lead. There's less torque from the engine. Any engine should be able to turn the front pump and converter at idle. When an engine can't do that, its because it doesn't have any power to turn them. A looser converter may slip more at idle rpms, but that would only reinforce what I'm saying is the core problem - not enough power.

The lack of power is even more obvious with a manual transmission if we treated them the same way. I think most of us have driven vehicles where you can put it in first gear without touching the gas pedal and the engine has enough torque to get the truck or car moving. Now if I can do that with some 1950s pickup at 500 rpm, and a hopped up 360 can't do that even at 800 rpm, which one has a more powerful idle?

Its the same thing we see with an automatic transmission when shifted into gear and the rpms drop alot. The reason rpms drop is lack of power.
Yes all the other things you wrote about come into play. But the basic issue was the engine didn't have the power.