If it were me, from Manahawkin I'd take the GSP south and then the Cape May-Lewes ferry. It's a bit expensive with an RV but worth the money if you've never done it. Then shoot out Route 9 to 113 south around Georgetown, and follow to the Chesapeake Bay Bridge-Tunnel. Then I-64 around Norfolk to US 58 out to I-95 at Emporia, VA and south from there.
The alternative is coming down the GSP, then go west on the ACE to I-295 south to the Del Mem Bridge, I-95 for a bit to DE 1 down to US 113 and follow as above, OR
Del Mem Bridge to I-95 South, then US 896 exit to DE 1/301 south, 301 to the Bay Bridge over to Annapolis, then 50/301 west to 301 SOUTH again, and follow 301 south to I-95 around Richmond.
The latter is a nice drive down through the Eastern Shore and tidewater Virginia, Fort AP Hill, etc and bypasses all of the******between Baltimore and Richmond. There is just a little bit of traffic around La Plata, but that's it. Otherwise, is four lanes of easy going.
Don't be in a rush. Over the last forty years, I've driven the NJ to Florida route about a zillion times, in cars, trucks and RVs, in winter, spring, summer and fall, rain, snow, ice storms, and 100' heat. The key is getting south of Richmond without having a stroke. Once there, it's eazy-peazy all the way to Jacksonville, where it starts getting messy again.
The problem, as you well know, is that there's no easy way from over on the coast, where you are, to the Philly/Wilmington I-95 area except for the AC expressway. That's one reason I recommend the GSP to the CM Ferry.