Shielding the guitar helps dramatically. All cavities & the back side of the pick guard. When I first started playing with Adamas picks it plagued my instruments. All are shielded now, and the problem is gone to the 95% level.
I had this problem before, and it ended up being my bridge ground. I was getting continuity, but the. Resistence was too high for a soild ground. I forget the exact number I was reading, but once I fixed that, my guitar was quiet again