Your route depends on where you are in Jersey. I live near tpk exit 9 and 8A.
I still go south on tpk to Del Mem bridge and from there stay on 95 or go south on 13 to 301, then hit 95 just north of Richmond.
Route 295 might work also to the DMB.
You said you're leaving in the evening so 95 straight down could work just remember to go around Balt on 695, the tunnel prohibits propane tanks.
Going around DC just FOLLOW SIGNS for 95 south, you will be there after most of the traffic. The GPS could send other ways thru DC, not good.
Make your arrival day the short leg, since you may be required to check in by a certain time. We stayed at Grassy Key last Jan. and had to be there before 5 pm.
The car is a good idea. There is a small parking lot on Simonton St., north side of Key West and close to Duval St. All day for twenty dollars.
South of the Border, Carolina Crossroads, Coastal Georgia are some overnight stops worth considering. We stayed at the Miccosukee casino, west of Miami on our last night before the Keys.
The ride down the Keys will be easy enough, since you know what traffic is like back home. We had no problems at all with the MH and toad.
Enjoy!!!