What you need to do is put the meter in series with the circuit you want to measure, not in parallel.

I did. I clamped the end of the wire to the mm and connected the other pole of the mm to ground.
IOW: reomote wire of the majestic amp is connected to an empty lead and a lead with the 1kOhm resistor. I measured the voltage on the empty lead with and without the resistor wire being connected to ground. After that, I switched the plug on the mm for current measurement and connected one end to ground and the other to the wire with the resistor. That's when I got the weird results. I'll do it again right now and see if I can make sense of it.