As above, you might not be able to access the ICW on a 65' boat. Many of the inlets have bridges less than 65', and the inlets can be shallower with poor charting, as the shoaling moves about with each storm.
On the other hand, with a big boat like that, you should be able to make a consistent 10 knots and, if you ride the Stream, 12 to 14, going outside. With that kind of speed, you should be able to make Charleston, SC in 2 days. That is an unencumbered inlet that can be sailed into, if necessary, and anchoring is allowed and safe.
The Chesapeake Bay Bridge–Tunnel entrance to the Chesapeake Bay is also a fairly easy entrance that can be sailed into, most likely with an anchorage in the area.
Then it's only a bit over 500 miles, or less than 2 days, to Newport.
You didn't ask, but I would recommend that you use your anchor instead of a mooring. Since your anchor tackle is the most important bit of safety gear you have on your boat, it should be safer than using a mooring with no guaranty or insurance.