I don't think potting is the issue ... that causes feedback between your amp and the pickup
In this case the wiring of your guitar is acting like an aerial, picking up radio transmissions. You could quite easily pick up police or ambulance radios too.
It must be that it is being cancelled out when you are in humbucking mode. I would work on shielding the guitar, starting with the control cavity and then the pickup cavity and the undersides of the pickguard (if that forms part of the cavities) and/or the control cavity cover. Make sure though that the shield is continuous and grounded to the back of a pot so that the charge grounds out into your cable. Be careful to avoid shielding close to the output jack and put insulating tape between the shielding and the pickups