Thanks to everyone who responded to my previous posting. A truly weird problem now fixed. George was on the right track with suggesting measuring voltage and amperage to the pump.

After the last go around when the fuel pump started to wheeze and the engine stalled, I noticed a small area of charred electrical insulation where the hood release cable passes the little 3 fuse auxiliary fuse box in the engine compartment on the driver's side. The hood release cable had chafed the wire, shorted, and was acting like a toaster coil. Further investigation showed that some insulation on the wiring harness along this side of the engine compartment was also charred with a few small bare wire spots.

As far as I know, this harness has nothing to do with fuel or injection so I can only surmise that somehow the hood release sheath short ran back through the whole system causing a voltage drop and excessive amperage draw. When the problem occured I was focused on the fuel pressure gauge and didnt look at either voltage or amperage gauges.

The solution was installation of a new hood release cable, which I had planned to do anyway, and a good cleanup and taping of wires and connectors. No fuses blew. Earlier today I ran the car for more than an hour. Ran just fine.

As to why the fuel pump started to wheeze and die after about 15 minutes running and would then run fine after 15-20 minutes waiting, my guess is that it took that much time for the hood release cable sheath to heat up to the point where it interfered with voltage to the fuel pump and then, once it cooled, the cycle could be repeated.

Thanks again for the input.

Something else to check...
For information....
This symptom is exactly like one I just encountered. The car would run fine for 10 minutes, then sputter and die. It would not start until it sat for about 20 minutes. This cycle would then repeat. In our case it was a plugged fuel RETURN line back to the tank. It was pluged and so the pressure would build and build until the pump could pump no more. Also it was noted that the car was not exactly runing fine put was running quite rich due to the increased pressure. After sitting the high pressure would bleed off and the engine would re-start.
Check the return line by plowing into it. It should be fee and clear (no back pressure) Yup I do like the taste of hi-test :)

One of the fuses in that little box is for the fuel pump.
That clarifies the issue a little - the short was near the pump
in the circuit.
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George Downs Bartlesville, Oklahoma