Can you restart the engine immediately upon arrival or are you saying the battery discharges while sitting for a few days? Can you confirm by disconnecting the battery when the car is parked? If so, try to isolate the culprit circuit. One way is to remove all the fuses and see how much current flows across each fuse socket. Start with the circuits that have courtesy lights, the clock, maybe an aftermarket radio or security system...

Are you able to inspect or test the voltage regulator?

Are you able to test the neutral start circuit?

My guess is the hum is the fuel pump.

Sixto
83 300SD
98 E320 wagon