You said that it is the law that your drivers license show your current address. This is not necessarily correct. Hence the comment. Also, no one is pulling your DMV records... it is irrelevant towards getting a mortgage. I also do not think a driver's license is required at all... just some form of government picture ID... I'm sure you could close with a passport. OP could claim dual residence with his parents and keep his out of state driver's license.... As long as he isn't lying to his insurance about where he lives I don't think this is any kind of issue.
My main point here is that I don't see anything here that will impede his ability to close on a mortgage.