If TIGHAR ever accomplished anything besides self promotion and spending a lot of other peoples' money and making unsubstantiated claims, it might be a possibility. Unfortunately, in the warbird world, they have virtually zero credibility,
There is probably only one company in the world that has the experience to make a recovery like that, and it wouldn't be cheap. Making the lift is the easy part. Prepping for the lift, loading onboard and being ready and able to do the necessary stabilization of the structure, is what makes it tough. Even the Navy doesn't recover any of the underwater finds that are going to the museum in P'cola, since they wrecked the PBM they attempted to recover in Washington state long years ago.