I had a similar issue years ago with a P25. Since Rega doesn't use a ground wire on the tonearm, I ended up getting the tonearm retired with the Incognito kit. That ended my issue, however I believe that Rega uses the right channel ground of the SE connection for ground. I did try an alligator clip before investing, that revealed the solution before I invested. So you may try that, as a note I have an RP10 with a Kleos and have no ground hum.
Good luck
Good luck