Use an expression pedal (such as the one built into the GR55 (and GR20, GR33 but not tested) to activate overdrive. The transition is the mid point of the expression pedal so you have to toggle the expression pedal a small amount in order to reset and then reactivate just like you would if you were tilting the classic controllers.
On the GR-55 you can activate the expression pedal for midi control by pressing EDIT > SYSTEM > MIDI/USB > GTR-MIDI and setting EXP PDL CC to 1 and bend range to 0. Other devices need to be setup so that the expression pedal works as a simple volume from 0 at min to 127 max.
If it works you'll see:
"Sending tilt up for overdrive!"
"Sending tilt down to reset overdrive." appear in the console output.