I was having similar issues on a fresh motor trans rebuild w/ 360 4speed with hays street strip clutch setup. One of the adjuster nuts on the levers loosened up causing it to not return to the same location as the other 2 fingers. With pressure plate still in the car I was able to move the one lever with my finger. Result was the pressure plate dragging on the disc slightly rotating the disc and input shaft.
Had to pull inspection cover and fork to look at the levers and diagnose. Since pulled trans, clutch, and whole package out. Deciding if I want to readjust lever stake stud and reinstall or replace as disc discolored (Blue heat discoloration)on the pressure plate surface in the same area as the effected lever. Good luck it took me a while to figure out my issue.

Now sounds like one time event, tendency to stall when clutch so perhaps not related to clutch depression at all. You mentioned heat soak and erratic idle and upon arriving home depressing clutch and engine appearing to want to stall.

Could be anything from mild vapor lock( unlikely unless really hot) to ethanol "enhanced fuel issue,,,very common on old carb powered cars,,,to old cars just being old cars and do what they do.,,,improper carb adjustment(fuel air mixture and or idle speed) timing, bad wiring somewhere in ignition system etc. Does car have AC?

Suggest to check this all out and note if and when occurs again,,,clutch depression incident could have been coincidental and sending you off in wrong direction for cause.