Have you thought of replacing the stock radio with an aftermarket radio? I got similar issue before and just replace it with an aftermarket radio from seicane, it works well for me. I hope you can solve the problem soon too.
I am thinking about replace my corolla stock radio with an aftermarket seicane S018604W shich seems to fit my Corolla well with gps navigation headunit. I have never done this before, anyone know how to remove the original stock radio? Thanks very much