Very cool to hear that it's probably still down there, but yeah, it's a government thing (actually a Navy Historical Center thing).

They are the folks ultimately in charge of all of the unrecovered Navy wrecks around the globe. With enough effort, I'm sure someone could talk the Navy into allowing the recovery of a selected aircraft, but it would have to be on the individual's dime, and the plane would still belong to the NHC following the recovery. I'm not sure I'd trust them not to show up the moment it reaches shore and confiscate it though. We learned a similar lesson when Doug Champlin made the mistake of trusting them as partners in a recovery. The result? A Douglas Devastator still rotting off the coast of Florida that had been otherwise okay'ed for salvage. The NHC shut him down the moment he brought them physical proof (a canopy) that the plane existed (proof that they had asked for). And as I understand it, the plane was ultimately going to be donated to the Navy Museum! Strange beast, the NHC.
With the recent change in personnel there, I imagine there might be a chance to revisit the idea of recovering some of the various submerged wrecks around the country and beyond, but it will no doubt still be a huge uphill struggle regardless IMO - bureaucracies and all.
FWIW, the oldest known intact F4U-1 Corsair is still sitting pretty at the bottom of Lake Michigan, no doubt serving as a king's feast for the zebra muscles, but otherwise "preserved". It would seem like a prime target for the new blood at the NHC to sink their teeth into, if they in fact wanted to signal a logical change in NHC policy.
Oh, and there's the somewhat substantial remains of Lt. Chuck Pilsbury's VF-17 "Jolly Rogers" F4U-1A still lingering at its crash site on Ballale Island in the Solomons. I spotted a photo of the aft fuselage and the star & bar with red surround looked like it could have been painted yesterday. Still the Navy's top scoring squadron of all time. That would seem like a no brainer of a recovery, and would make a great centerpiece/dedication at the Navy Museum IMO.