For anyone else reading this later, you can apply to both Marines and Navy boards. Marines call it contracting, but all it is is you are just getting the paperwork done before the OCC board. When I went through it my Navy recruiter said I wasn't bound to them at all and when I asked my Marine OSO, he wouldn't give me a straight answer so I assume my Navy OR was correct. I wound up getting rejected by the Marine board and picked up by the Navy board with no complications.
I would say just for everyones sake don't contract for a Marine board if you will get the results back from the Navy board between when you contract and when you find out if you got selected, just kind of a dick move. In my case the boards were staggered though. I found out the results of the Marine board before I officially submitted for the Navy.