A GCX and GCP would be great for this, however those do run up a bit in cost, so it depends on your budget. You could also use a Commander and Pedal Switcher, which is like a smaller version of the GCX/GCP combo. They allow 10 presets to be made with the Switcher's loops. So if I understand your setup correctly, it would be:
Guitar->ABY->Switcher(With TS, and amp channel switchers in separate loops)->Fender
So then you'd just program one preset with the TS on, and both channels on the amp to dirty, and another preset with TS off, and both amps switched to clean. This would use 3 loops on the pedal switcher.
I think this could also be done with the Controller and control switcher, but same principle.
Hopefully that makes sense, and I didn't confuse myself