Three weeks minimum
I don't see how you could do it in less than 3 weeks given the weather systems you'll face. I remember one day in the ICW when the wind blew 40 (an you imagine what Hatteras looked like then) and the waterway at this point was a giant lake when you couldn't see across. The sailboats slugging northward under power were getting killed by giant rollers coming from the North with the storm. If you are pushing yourself, the boat or the weather you'll lose. When bad weather comes, anchor out and exlpore in your dinghy. St Augustine was great if your on the outside, so is the Lauderale Yacht Club in Fort Lauderdale. Beaufort NC was nice place to stop not to far inside the ICW, when your outside and you gotta get out of the weather. Coinjock NC on the ICW has reasonable food and fuel with dock tie up. Nothing else anywhere nearby so everybody stops there. ICW there is a 75 foot wide ditch so no going at night as it's too dangerous, miss a marker and your aground.When sailing outside overnight use crew like an offshore race, preferrably 6 people two crews of 3 each. 3 on, three off, and keep going. Remember to reef early- especially planning for anything overnight. You don't want to be waking up extra crew to reduce sail at 3AM if you can avoid it. When you get bad weather sit it our clean the boat, drink a little and have fun.When we came North this May we had 3 great days in a row, got beat to death the fourth, and made a mad dash to beat the weather including one 14 hour day against the wind which I don't recommend if you can avoid it.Best of LuckBob KnottH380