This may sound off the wall but what kind of ELT do you have? I installed a new KY-97A and a new TPX along with rewiring my panel. I then had a similar issue as you describe, our radio tech suggested I disconnect the ELT at the antenna to see if that made a difference. The static went away. I reconnected it and it came back. Did it a couple of times, different conditions, same results. The radio tech said that older ELT installed in my ship can some how generate a signal that will interfere with the comm radio without being activated. I am not an electrical engineer, I don't know the minutiae the details.
I installed a new ELT, I have never had the problem again.
Mike was an old school radio tech, his nickname was Sparks.
A friend had a similar problem in his 182. I asked him about his ELT, it was a older unit, I can't remember which one. He disconnected it and the problem went away, immediately, he reconnected it and it came back. He changed out his ELT with a new one, and had never had the problem again.
This advice is worth what you paid for it.
Cheers,
Dave