I just reread your original post. 2000 hours with lots of time in tactical jets should get you hired by a major. You just need to go get your ATP in a Seminole and that will add your multi engine rating to your ticket. There have been plenty of SE only mil guys hired in previous waves with those quals and hours. Right now as it has been discussed on other threads, they are going through the "astronauts" and it will be a bit before 2000 hr TT guys get the call, even with the multipliers some companies use to help guys with all the high quality fighter/attack/trainer time.

This is a toss up, find a multi engine gig in one of the reserve components and wait for the majors to call. Pay for multi time to go to a regional to build 1000 hrs / year of SIC 121 time.

Look into the 340th FTG, they'd like you to live near the squadron, but you don't have to. We have done plenty of inter service transfers, and we send people to PIT with no prior experience of teaching at UPT. You have taught primary, so it would be an easy sell to tell them you wanted to fly the T-1. We have locations at Laughlin, Columbus, and Vance with T-1s. PM me or JetIP and we can point you in the direction, if you are interested.