If it was me, and I'm a total n00b when it comes to diagnosing fuel pump problems
I would first Get a voltage reading at the battery, they start the car and get a second voltage reading.
Turn the car off and probe the back of the connector of the fuel pump..... I think you're looking for a B and a L wire. If the multimeter has a hold or peak function, hit that and see what it jumps too.
Turn the hold function off and start the car and see what the voltages are. You should see 12ish volts at the bat, 11+ with the pump running and no start. High 13's with the car running and over 12 with the car running and the fuel pump pumping.
Next it's time for an Amp test. The connector needs to be unplugged but jump the gnd with a length of wire. Insert the multimeter between the hot wire and record the Amps, should be like 10-12A on the highside.
I'm betting that the volts are low or the Amps are high. If the volts are low, re-wire the pump and see what happens. If the colts are good and the Amps are high, than the pump is going bad.
The heatshields... I believe.... have very little to do with it. It's more a function of the pump running hard for hours on end and getting hotter and hotter and hotter and more and more resistance and blah blah blah things just get worse over time.
it could also be a clogged fuel filter or a bad fuel sock. Both of those things will lead to more physical resistance which causes the fuel pump to work harder and get hotter and the same thing can happen.
The key is to determine if it's a physical problem or an electrical problem. What's the inside of the tank look like?