I have this problem w/ single coils. I haven't had it with HBs. On my beloved strat I disconnected the bridge ground & it eliminated the problem with my system. Your milage may vary.

The trouble is that the guitar strings are tied to the grounding system (earth) through the bridge ground. The strings operate like a large antenna (2 ft x 4 in give or take). They pick up any RF signals in the area. By disconnecting the bridge ground the antenna is removed. You'll still have some antenna effect from the pickup wiring but it's small potatoes compared with the strings. I don't get any noise from it in my strat, but every guitar & system will vary.

If you have a simple method for removing the bridge ground give it a go. On a strat or tele it's pretty simple.

Good Luck.