Should I pick Gran Fondo or race?

Gran Fondo is what most Rando riders would suggest. That’ll likely set you up with sweet spot base, sustained power build, and a century specialty.

Lots of good commentary here: Audaxers / Randonneurs - Share your knowledge and experiences!

It sounds like you need to work on three skill sets. 1) Riding longer. 2) Handling heat. 3) Big climbs. Unfortunately, all three require you to just do more of those types of rides. Fun!

I’m a clydesdale of a Rando (over 200 lbs), so I feel your pain. Lower gearing on your bike will go a long way towards letting you go up hills without blowing up. And since buying lower gears is a lot easier than losing 80 pounds or gaining 150 watts to your FTP, that would be the path I’d follow personally.