Reply to Pitch Control and Master Tempo on the S4: what's possible?

I recently decided to scrap my CDJ's and move to a primarily digital setup (2 x Tech 1200's, S4, X1, TSP2), and have been primarily using the S4 out in most live situations where I am able.

Literally the only sticking point for me is how to manage pitch. While I understand full well how to adjust offset pitch faders on each deck, what I'd really, really like to be able to do is use either of the deck pitch faders to affect the master tempo only. For example:

1. The track master playing out is at 122BPM, and I'd like to keep that pitch constant for the next transition.
2. The incoming tracks normal BPM is 110BPM, which is no problem, because the sync button will get it there, regardless of the pitch fader.
3. Transition complete.
4. Now I have a track playing that is outside the range of the pitch faders, so any efforts to correct the offset pitch will always result in the pitch fader being pushed all the way down.

I'd like to be able to use a pitch fader in this situation to slowly adjust the output tempo, without having any sort of "tempo jumps."

tl;dr: I'd like for pitch faders to largely work how they do on track decks already, only I want them to affect the master tempo output only.

Anyone have any insights into this?

Cheers for any and all help.