Are you looking for riding roads or just getting there without I95?
I pulled up DeLorme Street Atlas, told it to avoid limited access and toll roads, and here's what it spit out.:
West from Morrisville on SR3014, then south on SR55. Turn west on US 64 and then south on US15.
It wants you to go west on SR73, south of Carthage, before Pinehurst. Pick up US 220 south to US 1.
Before Columbia (just past Camden) turn south on US 601, and pick up US 301 in Orangeburg.
It keeps you on 301 all the way to Ocala, FL, where you pick up US 27. Pick up SR 60 east in Lake Wales, take that to US 441.
441 takes you to Lake Okeechobee. Pick up US 98 on the southeast side of the lake, headed east again, to US 1 and south to Lake Worth.
I can't tell you about any of that north of Florida, but I can tell you that 27 south of Ocala is good road, 4-lane but not limited access, as is 441. 98 dumps you onto US1 just south of Palm Beach. It looks like most of that route is 4-lane other than the short SR cut-across pieces.
853 miles, 18 hours.
OTOH hand, using 95 it's 100 miles shorter and 8 hours faster!
(I've adjusted my Street Atlas to my driving habits, and accounted for real-world averages through towns, etc.
As for using some of I-95, and jumping off to do stuff and see things for a while, I couldn't make that work very well, esp in Florida. If you get off of I-95 in Florida, you are in congested traffic.