There's no option but to go outside as you pass the Jersey shore ( an overnight ). Take the Delaware Bay, the canal and head down the Chesapeake Bay entering the ICW at Norfolk. Take the ICW south till you get to around Beaufort NC, go out and continue south till you get To Charleston and go back in. When you get bored with the ICW go back outside. For us it was Beaufort SC. Go back outside and continue till you get to where you're going,, or,, go back in, perhaps at St. Augustine as it's a great city and motor down Florida. Go in, go out, go in, go out.
The ICW is a lot of fun and boring at the same time. Hence the inside/outside route (for us)
As far as time of year,,, April - June is the best but if you want to get the boat To Florida this year just go, see what happens and cary a big anchor.
There's no big 'approved plan' on going south. You just do it. Carry a few informational & ICW guides, play the weather and have fun. It should take about 2 weeks.
If you really want a captain to back you up, then just do what the captain says. If you're not having any fun doing the captains plan tell him you want to change the plan and ask for suggestions. Everything is adjustable.
SG is right though,, if you get a captain that sees it as a delivery, he'll go as fast as he can. If you can take 2 or 3 weeks to do the trip it's a lot of fun.