If you go to an FBO that is part 141 and VA approved, then you'll get your GI benefits. You can find regular FBO's who meet that criteria, not just a college/university. And yes, FBO's are often (not always) cheaper than colleges. Colleges will jack up prices to rediculous levels. Not all do, and I don't know what your school will charge...but there are many out there that do. FBO flying is well worth it. And through state tuition, you can still have your college paid for. See if your eligible for the GI kicker as well.
Good luck.