Engine stalling after be driven hard?

Do you know what is your compression ratio, or the pistons? If the CR is up around 9.5 or 10:1, then the slow-crank-then-fire may just be startup engine kickback when hot; that is not uncommon at all for higher compression engines with initial timing in that range. It will vary somewhat with the cam too, with longer duration cames being less prone to do so.

The rough running could be fuel boiling. Are you running pump gas? If so, try some quality 93 octane like Shell. If you don't have a carb heat shield, it may be time to add one. Take off the air cleaner right after shutdown when hot and see if there is vapor coming out of the carb's bowl vents. If, so, then for sure it is time for a carb heat shield.

And it could be other things. These are just a couple of ideas.