I have an idea for a workaround.
We used to confine all our Eb songs to a set for easier re-tuning, but one song really wanted to be in the standard-tuned set. But since it was so simple, (Song 2, Blur) I only tuned the low E down, then transposed the song, and just altered the way I played my 'Root-5' chords, i.e., an open E chord would be open 6, 1/5. No problem.
So for a live setting, where you need the sustain of a dead note, for just that section of the solo, why not use the Pitch Block, say down 2 steps, and just transpose a portion of the solo, and at that specific part, turn on the Pitch Block?
I sorta got the idea from working on some 7-string songs, using the Pitch Block for the lower portions of the song, but when the solo parts got into the higher register, I'd just turn it off.