You've got thousands of JK owners on Wranglerforum and only a few here ----- better odds of finding an answer in a larger sampling.
I've had two JKs, a 2008 and a 2014. My '14 has had the radio replaced under warranty but it wasn't doing weird things like yours.
I do have an electrical gremlin, have had it in for over a month at the dealership for warranty. They replaced the front window switches, the rear window switches, and the TIPM. Still there.
So I got out my multimeter and isolated it to the driver's rear window actuator. Will bring it in for a new one soon.
When I troubleshoot I try to find a middle area, break the circuit, and try to figure out which direction the problem is coming from. With a radio quirk it's harder to do....