I don't have an SDR rig, but I ran into ground loop hum too. In my case, I solved it by making sure that all the AC power connections for my gear did _not_ have a ground pin (i.e. they all had just 2-pin connectors).
I had a fairly simple setup to start with: mic, Xenyx 502 mixer, 31-band Nady EQ and a Behringer MDX1600 compressor. At the time I was using my Kenwood TS-850 and DSP-100. Everything goes to the same power strip. When I first plugged these three audio units in, I had terrible hum. Re-arranging the audio connections didn't seem to help at all.
But then I noticed something unusual: the Nady EQ had a typical 3-pin socket on the back for a standard 3-conductor AC cable, but the other end of the cable that came with it had just two pins -- there was no ground pin at all, meaning that the ground pin from the EQ was not connected. I thought this was weird: I'd never seen a cable like that before. Then I looked at all the other AC connections for the rest of the gear, and all had 2-pin AC connections, except for one: the Behringer MDX1600. The Kenwood power supply, the DSP-100, the Xenyx mixer and the EQ all had just 2-pin AC plugs.
As an experiment, I tried removing things from the chain to see what would happen. Removing the EQ had no effect: the hum remained. Ditto for the mixer. Then I removed the MDX1600 and the hum disappeared. Then I put the MDX1600 back in place of the EQ -- the hum came back.
Finally I put the EQ's 2-pin power cable on the MDX1600, and again the hum was gone.
So I put everything back in place and found an adapter to convert the MDX1600's 3-pin power cable to a 2-pin one, and then everything worked great.
I don't know if Nady purposely supplies those unusual AC cables with their gear because they know it helps avoid ground loops or if it was just a coincidence, but at least in my case that was what did the trick.
Recently I replaced some of my audio gear, and I once again ended up with one 3-pin AC cable in the mix, and sure enough the hum came back. Unfortunately this time I'd already used the adapter and didn't have another, so I resorted to the brute force approach of ripping the ground pin out of a spare AC cable with a pair of pliers. Once again, no more hum.
I don't know if this applies to your situation at all, but this was a bit of an a-ha! moment for me, and I figure it never hurts to share those.
-Bill