What you did worked out okay, since you made port without breakdown or injury.
I'm having trouble figuring out what your wind direction and speed was once it piped up. From the NW? And what was the 'canvas' you had on hand? With a storm jib and triple-reefed main, you may have had more steering control than with engine, but I don't know how strong the wind was. You should have some storm-worthy sails that you're not afraid of blowing out, since most boats handle rough weather better under sail than power.
I would think beam or broad reaching with just a storm jib may be the way to go, depending on the motion of the boat and the seas. If a NW wind, that puts you heading either NE-E on port, or SW-S on stbd. With the Gulf Stream a real concern, maybe steering south with minimal canvas would be the ticket? That way you're staying clear of your 2 dangers: the Fla shore, and the Gulf Stream, both then about 20 miles away either side.
But not to second-guess. The lessons learned were good ones, and you were taking the known dangers into account in order to come up with a strategy, which is the main thing.