I'm struggling with ground loop noise as you are. Mine is reversed from your problem. I have an unbalanced preamp (Schiit Heresy) and a balanced amplifier (Crown XLS 1500) and the noise is awfully distracting. I tried adding extra ground cables from the Heresy to the Crown and that reduced the noise by a few DB but didn't eliminate it. I have tried multiple different RCA cables. Nothing seems to eliminate the noise if I don't drive the amp with a balanced connection.
The problem, as with all ground loop problems, is the difference between the ground potential at the Heresy and the Crown. With an unbalanced connection, any variation in this potential is impressed onto the signal as noise (please excuse any inaccuracies as I'm not a tech). When I added cables to lower the resistance of the ground connection the difference in potential was reduced but the problem didn't go away. It seems that ground noise is not the only problem. I read about "pseudo balanced" connections which appear to be an option. The idea is to use a balanced cable that terminates on an XLR as normal and connect an RCA connecter on the other end, with the shield connected to the RCA body, the + of the twisted pair to the hot pin on the RCA, and the - of the twisted pair to a resistor that is the same size as the output resistor of the Heresy, in this case,100 ohms, to the body of the RCA connecter where the shield is connected. This balances the twisted pair and eliminates noise picked up in the cable (in theory).
I wouldn't be trying this if it wasn't for also owning a Behringer umc404hd which doesn't have any noise driving the Crown and AFAIK is using the "pseudo balanced" topology. I just need to pick up some microphone cable and a few connectors to give it a try.