Sounds like something a ground loop isolator might fix, but I don't know why that's happening or how you'd fix it. Maybe an aftermarket radio would take care of the problem. Sorry I can't be of more help, I'm dumbfounded.
1996 Grand Cherokee Limited 4.0L
PSC Steering Gear; NP249 w/ new VC; Moog TRE's, Track Bar, Stabilizer bar bushings and endlinks, control arm bushings
Still no lift, and almost no paint on the hood