Have you measured the pressurized line(injector rail inlet) with a gauge, it's possible your FPR is failing and bypassing too much fuel back to the tank, thus not having enough "push pressure" to get the correct amount of fuel thru the injectors when they open.
The fuel pump should not run continuous without the engine turning.
Older Jetronic control systems power the fuel pump when the start button was pressed, and then the pump continues when the controller detects engine rotation signal from the HES sensors.
Newer Motronic systems "prime" for about 3-5 seconds when key is turned on, then pump turns off until engine rotation is detected by the HES sensors.