I wish I would have found this sooner!!
This is the exact problem I was experiencing for a whole summer. It seemed to happen mostly on hot days, so I suspected vapor lock. As soon as I let the engine cool for 30 - 40mins it would restart and run fine. But the hole time it was a broken wire on the fuel tap solenoid. The wire shielding was still slightly connected so it look as though it was fine, however inside the wires were broken. So I temporarily fixed it by removing the o-ring on the solenoid, which worked. However I was worried that it might still be limiting my fuel flow and if I needed to take the tank off it would run gas every where. So I needed a manual fuel tap, but I didn’t even consider going to my deal because they are pretty worthless and never have a clue what they are talking about. Instead I amazingly found this little hydraulic needle valve (dynamic fluid components, p/n DKLN125N*1/8NPT brass needle valve), that once unthreaded from its housing threads perfectly into the v11 fuel tap!!! I did however have to turn a little radius on the tip of the needle to hold the o-ring, I used a machinist lathe, but you could do the same thing with a dremil if you have steady hands. I also used a little tread sealant on the threads just to make sure it would not leak and all my problems are solved, no more vapor lock issues and I now have a manual fuel tap/ petcock.