Try first confirming that you are also losing fuel pressure when the car stalls, and the gage reads incorrectly. You'll need a fuel pressure gage connected to do that. If you have fuel pressure when the stalling occurs, then you are actually dealing with two seperate issues. If your losing fuel pressure, then you might be dealing with a common issue and further testing will reveal if that is the case. I'd test the ground circuit for the pump, as well as the sending unit for an excessive voltage drop, and also measure the current flow through that circuit.
Are there any codes setting in ANY of the vehicle's modules? You really need to pull codes from every module on the car with a problem like this, and few tools access all of them except for the factory tool.