I've noticed a few resorts that we've stayed at will rent out units on a day by day basis, our St. Augustine Beach one included. I would call the resort today and ask about the possibility and the cost. Explain your situation and ask if you can book it via email if you need it. I know ours charges a cleaning fee (since the chances of a person staying in the same unit as they have booked are slim) in addition to the rental fee. For that reason, the few times we have arrived in town a day early, we get a cheap motel for the night for less than half the cost.
~Diane