I'm also going to answer my own question! I returned the TT to GuitarGuitar and they managed to fix it by performing a factory reset. The procedure is different from what's described for a firmware update - I followed the instructions for "4 tone lights flashing on AMPLIFi". The factory reset is actually described here: Line 6 Device Factory Reset Procedures.
In summary, power up while holding Tone and Volume buttons.
