There are a couple of options. The easiest with your current setup might be to set a certain Program Change number to BYPASS on all three units. Then you could send that Program Change number from the MIDI Moose when you want to Bypass.

You could also Bypass all three Eventides via an Aux Switch connected to one of them, but in that case you would need a MIDI Merge box if you still wanted to use the MIDI Moose.