Most woodworking schools of short duration I know of, are project related. The class is for one project in a set amount of time. Some times it is one full week of very long days, in order to finish the project. Some times, just a weekend. I don’t know if any work with the GI bill. Most are set up for “hobbyist”. Here are a few more to look at, within a days drive of you.
The first two are in Minnesota. North House Folk School is right on the waters edge of Lake Superior. It is just beautiful there. Mike Siemsen is also in northern Minnesota and a very good instructor.
Mark Adams is just outside of Indianapolis and has a wonderful shop. There are more, if you look.
You can also buy DVD’s and get a lot from them. I have also used Craftsy. Jeff Miller has a very good class on a shaker night stand, I think I got it on sale for $20, with unlimited access.
Good luck with your search, and thank your service to our country.