360 Questions.. pardon my ignorance.

With it stumbling at hot idle should I first adjust the speed screw or the base timing?
That’s fuel related.

Once base idle is established do I adjust the mixture screws for best idle/vacuum before bringing the vacuum can back in?
The vacuum advance will have zero effect on idle if on ported vacuum (where it should be for a relatively stock engine) so you’d want the idle fuel and timing sorted out prior to adding it back in to the equation.
After all that, I confirm my total timing and limit the distributor weights if necessary?

Yes and adjust the curve with springs. And I’ll add that once vacuum advance is added back in, you might have to delay it with the screw in the can to avoid detonation on early tip in at cruise.