Ok, so the issue comes from my pedal monstrosity. If I plug directly into the amp from the guitar, standing right in front of the amp, with master and channel volume at 100%, on the gain channel, I do not even get regular feedback!
When I am plugged into the pedal monstrosity, the squeal is deafening with my wireless pack off, but disappears as soon as I pull the cord from the input jack. All is well with the amp...but not with my pedal excesses.
Also, it was unfair to say that I was getting the squeal with "no guitar signal". By this I meant a cord in the input jack, but the wireless pack off. That is NOT a lack of input.