I can't speak from personal experience yet, but I am about to embark on the same adventure as you in using my GI bill for my ratings. I do not think it is unreasonable at all to ask for another CFI. I am about to finish my PPL and have had 8 different instructors due to most leaving for the regionals or moving. It is "your money" you earned technically and you should be getting quality training with it. Is there someone at the school you can talk to about it?