Before you go broke hiring lawyers, and filing claims, do some more homework.
If the wreck is within 3 miles, like it or not it belongs to the state at the moment.
I'm not trying to diss your wreck, but it is highly probable that others in the past have knowledge of your site. Whether it's local sport divers, fishermen, history buffs, or State Archaeologists there is a fair chance that someone else has checked it out. People have been dragging nets & trawls, diving, and fishing for a lot of years over a lot of ocean, yours is by no means remote. Just because a site isn't advertised on a chart, at the local dive shop, or on google doesn't mean someone doesn't know about it, keep digging, talk to local fishermen, see what the State knows.
My suggestion would be to filter through your state's bureaucracy and find the department that handles underwater archaeology. Most have reams of documentation regarding known wrecks in their waters whether they've been located and explored or not. I would start there and quietly see if you can figure out if they have visited or are aware of "your" wreck. You may be surprised, most states don't have the money to go out wreck hunting, they usually have other things that take up their time and budget. The historical significance you suggest is present should make your wreck historically valuable (I don't mean $$$) I mean historical knowledge. PS - Museums don't typically buy artifacts from treasure hunters, they are part of the same political club as the archaeologists and are also subject to being harassed by their peers.
You really need to determine your interest in pursuing it and figure out what you hope to achieve by pursuing it. If it is solely one of monetary gain, I'd would reccommend you find another means that will provide what you seek. Either that or start buying Lotto tickets or learn to count cards and move to Atlantic City. If you are interested solely in learning more about the history more power to you. I think the days of pillaging historic wrecks inside three miles and selling your finds are numbered. I really think people have a bad habit of getting caught up in the romance of "treasure hunting" and overlook the political and economic issues. Your facing an expensive uphill battle to do these things, anyone who tells you otherwise needs to actually try it sometime.
I honestly don't know you or your motivation, and like I said I am not trying to take a jab at you, or criticize you, I'm just keeping it real so to speak. If you envision making a fortune off rare shipwreck artifacts on EBay centered around a wreck in State waters that George Washington took a ride on, and doing things on the cheap you might reconsider and save some frustration.
Good luck what ever you decide. Someone else suggested it, read through some of the older threads, there is a lot of knowledge here. Keep in mind most seems biased toward half hearted endeavors that likely never got started or successfully finished for one reason or another. You usually don't find a lot of "I'm done with wreck hunting" threads here, some people just fade away, or shut up once they learn a little more, a few keep at it. Unfortunately many have come before us and done more harm than good for the resource. There are exceptions though.