Hey Bill,
If I were you I'd just leave that tree to do what comes naturally. I'm only saying this because I'm familiar with your climate. I lived for 10 years just about an hour SW of you in Naples. Granted, that is a full agr zone away but consider this. All the citrus down there is just ripening this time of year. Most of the citrus grown in FL is grown in the central part of the state and citrus is far less hardy than figs.
I could be wrong but if it were me I'd just wait and see what happens. I guess my only concern may be just what you're thinking. That is, will it mess the tree up when you do get a frost? I suppose I wouldn't know any more than you on that. Maybe someone here, who's dealt with a similar situation, will offer some advice.
One thing you could do is build a makeshift "greenhouse" large enough to just set over the whole tree whenever you here that there's a threat of frost on the way. Something as simple as a frame made from those little 1 X 2's (I think they're called ferring strips) covered with some clear plastic might be just enough to protect it until the frost passes. Some of that clear plastic used as a painters drop-cloth is usually pretty cheap at any home improvement store. I don't know how big the tree is but maybe one of those large clear leaf bags would be large enough to do the trick.
So, if it were me, I'd break out my screw gun, a box of screws, some ferring strips, my staple gun or box tape, and some painters drop-cloth (or clear garbage bag). Then then I'd get my fig fork and knife and hope for ripe figs man! In your zone, I don't think it would be an impossible hope. What do the rest of you think?
-Bill.