You could try this:
Go to Menu - Effects Edit - TFX (bottom of screen)
Scroll left until you get to Audio Input.
Under Audio Input Output Assign, change it from Main to Sub.
I've not tried this but my hope is that when you assign it to Sub, you won't hear it to monitor it.
I just tried an internal sound, and when that's set to Sub output, it's muted (though I will say I can *barely* hear it, and that might be becuase the reverb is set to 20 and I might be hearing some of the EFX bleeding through - scratch that, I just tried it again and that's what it was - I turned the Reverb off and voila - the Sub Output is silenced.
But the MIDI is still being passed to the DAW (so USB MIDI is being sent).
I only have Headphones, which monitor at main.
I'm thinking with Audio Input, it's going to go USB to the DAW, come back, and then you'll hear it (because in the next tab over, there's a USB Audio output selection too).
You could try the next tab too and see if some combination of routing one or both of the USB outputs to Sub instead of Main keeps you from hearing that version while you play.
Gotta run else I'd try all this.
That's about all I can think of at present, but maybe that'll give you some ideas.