Sure sounds like vapor lock...
https://www.prestigemoto.com/hardcore-tech/blog/vapor-lock-and-how-to-avoid-it.html#gref

My old 'F100 would have a hard time starting when the engine was hot.  It took me a long time to figure it out but it didn't get any airflow under the hood.  The headers got hot under there.  Eventually I added some vent holes in the wheel wells but I also never had a problem once it was running.  

Yesterday the car would run fine in the garage, after 30/40 minutes idling with the hood down it would stall out. Carb was EMPTY at that point

Today I bypassed the tank, all the lines along the frame, I also removed the fuel filter and put a T in so I could watch fuel pressure. Pressure was 5/5.5

I made a gravity feed temporary fuel tank out of a paint can and ran a hose directly to the pump inlet.. I put a fitting in the bottom of the paint can I hung the can from one of the hood latches, so fuel would naturally run down to the pump. The car ran for an hour. Then I ran it again for an hour and fifteen minutes no problems and fuel pressure was consistent.

This was encouraging BUT I wanted to see how it would react if the pump had to do all the work. I raised the car and ran a hose into a can under the car. Still no tank, no hard lines, no hose from hardline to the pump, no filter. The car started and maintained 5 pound of pressure. After 30 minutes the idle started slowing down, but for a few seconds the pump was still at 5 pounds.............a few more seconds the fuel pressure gauge started fluttering, the car stalled and the carb was empty.

I am going to try my spare carb because that's the only thing I haven't changed.  I am in NJ and the temps have been in 60-80 degrees during this time period.  Last August I drove the car for 2 hours in 90 degree weather with the AC on without a problem

I had a similar problem with my 1955 XXXXXXXXXX.  I fought with it for a good part of a summer. Turned out to be piece of something that appeared to be Saran Wrap. It would drift up against the fuel outlet and plug it.  Then the fuel line to the carb would be dry.  Opening the fuel line at the carb apparently broke the vacuum and the "Saran Wrap" drifted away only to plug it a few days later.  
We were in high school at the time and didn't have a lot of car savvy, but we learned a lot about fuel systems from that.
You said you replaced the tank with a new one.  Did the problem occur with the old tank, or just the new one?  If was with the old one too, you would have to assume it wasn't something floating around in the tank.
Good luck solving it.

Don

RossL

Sorry, I missed your last post.  You've gone beyond the tank being an issue. 

Don

What has been changed since last August?  
Can you try a different fuel pump?  

Quote from your last reply ~ "The car started and maintained 5 pound of pressure. After 30 minutes the idle started slowing down, but for a few seconds the pump was still at 5 pounds.............a few more seconds the fuel pressure gauge started fluttering, the car stalled and the carb was empty."   Could it be the needle stuck or sticking closed in the seat?...  Stig. 

Is the gas cap vented?  Try running the car without the gas cap.

Is the gas cap vented?  Try running the car with out the gas cap.

I've tried two gas caps and even tried no gas cap.  This did not change the out come.

I have two rebuilt fuel pumps.  They both are doing the same thing

I changed out the carburetor in November.