I would do the simple things first.
since you have a mechanical pump, I would just check for accelerator pump squirt first when you have this issue.
it could be as simple as boiling out the carb.

BUT since you mention no matter what it takes about 20 min to restart, I would look at ignition first.
Check for spark when this happens again. carry a spare plug with you and just pop a wire off and run it up and see if you get spark.
my bet is no.
then you have to see if it is the msd box or just the coil.

I have to ask if you run it up to temp and then shut it down again, do you still have that problem?
or just after the first time?

any extended driving?