Is it possible that the sticking point is holding a Florida driver's license? If you surrender it and get an Indiana Driver's license, it might help to establish residency, at least in the eyes of the people looking at the paperwork if not the law.
Short answer is yes but that is because in order to have a IN drivers license, I must be an IN resident, in which case I must not claim FL residency and therefore cannot vote in FL, which means I'll wait until the election has passed.