First things first.
It is not just our Atlantic shoreline, rather the whole Chesapeake Bay.
Anyway, let us try wind (not to mention solar) before, which ought to crowd up the place enough.
Further, I see that former exploration showed no result.

The Navy does not need the entire offshore area to do their training, they have the entire Alantic Ocean. I few oil or gas riggs off the coast will not effect them.

Drilling is a national security issue and a primary method of restoring our balance of trade and some economic sanity. They have to be able to coexist. I remember someone saying something about hanging together ... or hanging separately. I think it applies here.

the Navy burns and needs lots and lots of gas for their testing, training and operations. We get much of it from our rivals in the Middle East. Why not conduct operations a bit further out. The Navy is constantly altering course due to underwater hazards and or polical concerns. Drilling somewhere is the only way we will ever get off of our dependence on foreign oil. Redesignate operational and training areas to accommodate the effort. How difficult can that be?

Let the state continue to investigate/research, they might find the same results as the Navy. But I don't believe the Navy needs the entire offshore area to carry out their missions/training.