From memory, without log handy... and not counting our lay days for sightseeing or weather or whatever... we made it 8 legs from Portsmouth to Myrtle Beach... at a very leisurely pace, mostly 8 knots or so, and short days. Segments were:
Tidewater Marina to Coinjock
Alligator River Marina
Myrtle Beach (Osprey in Socastee)
I'd think you could at least halve that, assuming halfway decent weather and no issues through the Lejeune firing range, etc.
Outside from Beaufort to Wrightsville Beach, and then from Wrightsville to Southport could let you take more advantage of your speed... weather permitting.