Yes you can go through the tunnel. They will stop you and ask you to turn the tanks off and mark them with a tag. If you are not interested in time it is a different way to go but no a fast one.
I would suggest 95 into Delaware to 896 south, 2 miles past the rest area, 896 becomes 301. Follow 50/301 through Annapolis. About 19 miles from the Annapolis 301 turns. south. Watch for it or you will be in WDC. Take 301 into Va. and follow it south from Bowling Green to 295 around Richmond. This route takes you around WDC and Baltimore and is a nice country drive. The posted speed limit is 55 but most of the truck will pass you if you do.
I generally run a longer day than you are planning and use Wal Mart or Cracker Barrel instead of a campground. However I would not suggest that in southern Fl.
WBCCI 12156 AIR 3144 WACHUNG TAC NJ6
2004 Excursion 4x4
1991 34 ft. Excella +220,000 miles, new laminated flooring, new upholstery, new 3200 lbs axles