So it turns out Big Slick is one of the pilots that I manage. For those of you interested in volunteering for an MC-12 (or any particular deployment for that matter), please contact your MAJCOM Rated Manager, Rated FAM, or MC-12 FAM.
Which of those, or what they call themselves depends on the MAJCOM. The FAMs that handle deployments are usually in the A3, most often in the A3T. There is also a MAJCOM assignments and career field manager for rated officers that is usually in the A1. They don't handle deployments, but can likely point you in the right direction. If you can't find any references for your particular MAJCOM, PM me.
Side note, if you're on a joint tour, don't bother calling. You can only be deployed ISO your COCOM, and the waiver authority is SecDef.