I have done the trip from and to Florida numerous times at the time of year you plan to travel. My best advice to you, considering the boat you have, is to not go outside after October, and even in October you could be pushing your luck. A Catalina of that size is not a boat you want to be in with a northern wind pushing against the gulf stream. If you have to do it, make short runs, after monitoring the weather, on the outside with a stop along the coast of S. Carolina, then go inside behind Cape Fear so you don't have to go around Frying Pan Shoals, go back out on the other side of Cape Fear and cross Onslow Bay. Then go inside at Beaufort and take the Intracoastal up to the Cheasapeake.
A longer yet safer route is the intracoastal waterway all the way up.
I would leave the inexperienced crew on land and take someone experienced if you decide to go outside at the time of year you plan to head for the Chesapeake.