Not a good time to go and the added complication of stopping in St Augustine does not help. The first consideration is what condition is the boat in? If it is truly ready for offshore condition then the best way to do it would be direct to Delaware or Chesapeake Bay assuming that there are no tropical depressions even forming anywhere - then go hard using the Gulf Stream if possible. Do at least a couple of test sails before you go - good if you could have one when it was blowing a bit (20-30 knots).
You could go in a series of shorter trips through Puerto Rico, Dominican, Bahamas to Florida but you are exposed to hurricane season for a much longer period of time this way and sooner or later you are going to catch it I think and there may well not be anything resembling a hurricane hole to duck into (and you would be arriving there after everyone else has taken the best spots.
You might want to consider the use of a weather routing service (Chris Parker?) for this trip too.
My preference would be to bring the boat north next spring but I can understand why you would want it sooner.
Finished the circumnavigation in early February in Grenada. Have to work on a book project for the next several months so the boat will be waiting for next year.