I was reminded of this topic and just got done poking around in the sim. Using the Behavior tool I can see the LVars, but not anything that would be useable inside the sim. I didn't see the AP Pitch Reference, either, which tells me that it's probably wired in under the hood and not tied to the switch/animation, so this likely wasn't a good test anyway.
If you think you've exhausted the list of possible sim bindings, and I'm sure you have because I just searched "reference" and I didn't see one I thought would fit, either, I would give someone official from JF a few days to pitch in here, or maybe open a support ticket. At least then they can log it for potential inclusion into a future patch.