Which fuel pump is causing intermttent engine stalling?

1986 Volvo 740 Turbo sedan

Problem: whilst driving, especially in hot weather, the engine dies. If left for 40 minutes or so, engine restarts.

Questions:
1. Is it likely however, that this is a relay problem? If so, which one, as theres 2 relays.
2. Could there be rubbish in the gas tank that periodically blocks the outlet?.
3. What is the purpose of the low pressure fuel pump in the gas tank? I have been told its only purpose is to prime the external high pressure fuel pump to make cold starting easier/quicker.
4. Are there any tests that can determine which pump is causing problems? Do the symptoms below id whats causing the problem?
5. If theres a problem with 1 pump, should both pumps be replaced?

Symptoms: When it is going to play up the engine first stutters coming out of a corner. About 10 minutes later, the engine starts to miss, making a plut, plut noise, the turbo gauge goes heywire as the rev counter slowly drops before the car comes to a halt. All red warning lights come on. Although engine will crank over and theres spark at plugs etc., it refuses to go until its cooled down. Theres no woosh sound when I undo the gas filler cap. The frequency of this intermittent stopping is increasing - but never happens when the cars with a mechanic!. Last time it stopped, Xmas eve, it was diagnosed as a fuel pump problem by an NRMA serviceman. He recommended replacing both pumps. This will be a $500+ job in parts alone.