Looking for recommendations on a somewhat uncommon career progression.

I started my flying career with the Air Force Reserves, currently accruing international right-seat heavy jet time at a rate of ~30-40hrs/mo. Have about 400 total in the logbook, considering options for how to most rapidly progress to an eventual job with the majors. Would you look at a regional to get the ATP paid for? Stay flying only mil, upgrade to left seat to get some PIC, and wait it out until eligible to go right to a major? Other thoughts on efficient ways to build some TT around the 750 ATP-R timeframe?

The experienced folks in the squadron have given some input, but most came from AD and arrived on the reserve side with all of their requirements already met. Curious to hear your thoughts! Thanks in advance.