340 has a hard time starting when hot?

Yeah, if it's turning over fine with the starter, it is not heat soak.

My Sport Satellite had the same exact symptoms & it does have a mini-starter.

The fuel would boil out of the bowl after driving an hour or more & then letting it sit for a car show.

Once I figured it out (those long cranking sessions when trying to leave a car show do attract attention) I started using an old mustard bottle with gas in it to fill up the fuel bowl manually before trying to crank it.

In my case, switching to non-ethanol cleared it up with no other changes.