We have 17 King Air 300s and 6 Challenger 605s. The King Airs are divided among the 5 regional offices (Sacramento, OKC, Battle Creek MI, Atlanta, Atlantic City) with about 3 in each location and the remainder in OKC (usually in some type of maintenance or phase inspection). The 605s are all based in OKC but are used primarily for international work and some domestic work.
Checking the IFP Gateway:
https://www.faa.gov/air_traffic/flight_info/aeronav/procedures/ , it shows the new procedures at GKT scheduled to be published 4/15/27. So definitely not 3 years, more like 16 months from now.
The issue isn't the availability of flight check aircraft, it's the behind-the-scenes work that goes into the runway survey data and developing the procedures to the new runway location. It's just an assembly line, with lots of work to be done and the fitting of the new procedures into the development pipeline. Whether 16 months is reasonable or not is a matter of opinion, of course.
While I don't know anything about GKT specifically, I will say that the best and most timely results I've seen has been when the airport manager (or other proponent) starts working with the procedures teams EARLY - like way before construction even begins. That way things can get rolling and scheduled simultaneously with construction. This isn't always possible, of course, but the earlier things start, the better. For example, when GKY added their new runway 1/19, I flew a flight check of the procedures in maybe September or October of 2022 - this was after the runway was physically there (so the actual, as-built coordinates were known) but before any of the striping or lighting was installed (though they were working on it). The new runway was opened effective the same day the procedures were published in November of 2022. I do believe the procedures were temporarily NOTAMed NA at night until we could get back to check the runway and other lights - remember, those hadn't even been finished yet when we flew it. But that meant that in this case, there was literally no delay between opening the new runway and having the new procedures published.