Any update? I second that, I ran my 12volt and ground straight to the battery to the CB. Also make sure you have your antenna properly grounded assuming you are using a ground plane antenna which most people do for Jeeps. Here's a video on antenna grounding and set up of the washers for the antenna mount.

 

One thing this guy didn't do was show if the spare tire hits the antenna because that could throw off his SWR. But agree with how he set up and checked the ground as well as making sure the insulators for the stud were actually insulating the stud from ground.

Also looking at his tire carrier, I think I would have fabricated an L bracket that attached to the 3rd brake light mount and put the antenna above and away from the tire. I'm not a fan of the location of those CB antenna mounts that attach to the door. If you forget to open the door fully or you are on an incline and the door starts to close slightly a longer antenna will hit the back window glass when you open it.

As for the OP's problem, I too would remove that booster as I suspect stray RF is causing the malfunction. Booster is probably poorly shielded.