Yes replace the J85's with the small Turbofan of your choice, either in the same thrust class with dramatically lower fuel burn or go bigger(?).
FWIW someone has a retrofit kit for the old L-39's to a new Williams Intl engine. Same thing, older airframe, new engine....
http://www.l39ng.com/#about
Wow, yeah! A pair of those in the OA-37's air frame might be a good idea. In addition to those engines, they could modify the cockpit to make it a single-seat version. It has great visibility with the canopy that it already has and they wouldn't need a T-37 for training, either. I'm fairly sure the wings and air frame are strong enough for carrying and launching Mavericks...among others.
