I would speak with a mortgage lender in detail about your situation. I would go with a mortgage broker who works with a number of different banks and lending institutions. I can refer you to someone if you are interested.
Unfortunately, they go by credit scores in order to refinance. Also, it would not be good if you are ever late on your mortgage payments. I am not a lender, but I do know very many of them and would be glad to refer you to someone.
JD - I work with a mortgage loan officer who has connections to nine different banks. If it can be done, he can do it. If you're interested, I can put you in touch with him. My email is email@example.com.