earth-ground the RME in some way. Like it was before when connected to the amp.
You could connect the earth wire of an RCA cable to the 230V ground - if one of these jacks were free:
LINE OUTPUTS / SPDIF COAX
The housings of my equipment in the rack are connected to 230V earth via plug contacts in a star configuration. I use a screw on each unit for this purpose. With the ADI-2 DAC FS it is the screw at LINE OUTPUTS.
The hum disappears when the unit is turned on and returns when the device is switched off. In my current configuration, the ADI-2 is connected only to CD transport via optical cable and the standard power supply.
It's a "special function" that gives you an overall result:
(1) How well you can still hear (dynamic range).
(2) How badly the soles of your shoes separate you from the earth (floor).
(3) How high the leakage current (= low leakage resistance) of the headphones is.
(4) How high the leakage current of the power supply is.
(5) Which power supply you are using.
If you want to know more about "the problem":
To (2): Use rubber bathing shoes.
To (3): Use insulated headphones.
To (4-5):
After getting new equipment, I always look at the waveform of the DC power supplies on the oscilloscope. The original power supply of the ADI-2 DAC FS has an extremely distinctive, low-frequency signal that changes strongly with load (unit on). I have never seen this signal shape before. My power supply is installed in a rack, so it is too time-consuming for me to repeat the measurement and post photos of the power supplies here: ADI-2 DAC FS / old ADI-2, ...
the power supply injects a tiny amount of mains noise into the ground (reference) potential
So if it was only noise, you shouldn't be able to hear anything.
If you want to try a different power supply, make sure it has sufficient power: The ADI-2 DAC FS has an inrush current >> 1 Ampere.