T1000-1bdcp

Is the rail voltage changing because the output stage is switching on and off?

Are you saying that the 10uF didn't reduce the noise on the speaker terminals?

To get an accurate view of the waveform on the speaker terminals, you may need to connect the ground wire for the scope probe to the negative speaker terminal.
 
Don't use the gain as a level controller for testing. When troubleshooting, you need to change only one variable at a time. Using the gain involves the gain control and circuit.

If it does this with no input, nothing connected to the RCA jacks, you need to find what changes when the gain control is adjusted. More noise on the output?

Is the output stage switching on and off as the rail voltage changes?

Is the amp producing audio?
 
If you have a speaker connected, the hum could be causing the additional current draw.

The rail voltage is going to drop to 0v. If it has the common 3k ohm drain resistors, the voltage is going to drop. How long does it take to drop to 0v after the remote voltage is removed?

Does the hum stop when the rail voltage goes high?