No Fuel Pressure after driving car.

I like to point to the rear jumper from the in-tank pick-up to the hard line. The factory puts band-clamps on these which work for decades. But when most guys replace that short line, they use gear-clamps. Well gear-clamps introduce two little areas right next to the screw-receiver that tend to not seal. Because the jumper is higher than the fuel in the tank, it doesn't leak gas. But the pump can easily suck air there.
If I have to use gear-clamps anywhere on a fuel system,I use two per joint, and stagger them 180*. Mostly I won't use them. If you do it this way, you also do not have to tighten the clamps to nearly squeeze-the-chit-outof-them.
This same thing can occur right at the jumper next to the fuelpump. However this one can leak fuel.
And I no longer install a filter on the pressure side, choosing instead to run the hard line with smooth shallow bends,all the way to the carb.

If the engine stalls, and you have no pressure after driving one mile, and the tank is properly vented, then it has to be one of four things;
1) the float bowls are empty, and the valves are hung open
2) the supply line is full of air,or severely restricted, or
3) the pump is not working properly
OR
4) the engine is flooded, due to hung-open floatvalves, as in defective, or possibly compromised with debris.
I'd be doing a fuel volume test. I would fill the carb bowls, redirect the pump-output into a tip-over proof container, and measure the pump output over 30 seconds at 1000 rpm. Then compare that to it's spec. I would run the fuel thru a section of clear line and watch for bubbles. Or if a clear line is not available,I would be sure to keep the delivery end submerged in the fuel,and watch it closely for bubbles. I keep the collection bottle higher than the pump, cuz the bubbles will exit better.
In your case, I would mark the collection bottle as to the liquid level,at the 30 second mark, and continue to run the engine to a stall, still watching for bubbles, and continuous proportional output. I would also run a timer to see how long the engine will run at 1000 rpm on only the fuel in the bowl.

If this proves to be OK, then I would pressure test the valves, starting at 6 psi and working to 10. If they blow off or leak, replace them.

But if the valves hold pressure and the pump is not sucking air or failing to deliver adequate fuel (and the tank vent is working);then I would look into fuel boiling. In your case, if the fuel was boiling in the carb, enough to stall the engine after just one mile, then fuel vapors should be pouring up from the airhorn. This would be a dead giveaway to bad valves or boiling fuel.

But I just have to add; my 367 running at 205*F and with aluminum heads,uncoated TTIs, and with a 7-blade thermostatically clutched fan, phew, puts a tremendous amount of heat into the underhood environment. I have taken no steps in trying to keep the fuel cool, other than,I do have an AG manifold and fresh air into the carb. And I never have fuel problems, not since 1999. Mind you our hottest summer days here rarely exceed 38*C, or 100*F. But I don't see that as an excuse, cuz the underhood environment will be at least 2.5 to 3 times that and possible 4 times, for brief WOT periods.