http://www.nacac.org/howtoadopt.html gives you some information on State Fostercare and adoption. Is it impossible to move off base? Maybe not tomorrow...but eventually? Also did the agency say you could not adopt if you live on base or just not foster? Because you can start the wheels in motion for a state adoption, It takes a while anyway. You can be part of the 25%.
Also, if you adopt older than an infant overseas, you can adopt for less than 30k. You can also adopt from some countries for around 12 to 18k, and you get the tax credit.
I think there should also be someone on base that can help you, a social worker, or lawyer, and possibly help with finances.
If you want to adopt an infant domestically and want find your own match, there are methods of finding someone. (I adopted an older child through the state, so I will let some one else give you that information).