Can you buy the "residue" back from the insurance company, to part out? You might be able to find a project more easily than a complete plane, and use your current plane as a donor.
However, I'm trying to correlate "flyable" and "substantial damage" . . .
What Keith said - the insurance company will pay you the agreed value, then take your plane and immediately put it up for salvage auction. You can always bid to buy it back. If you win the bid, great! You probably won't have to change the registration (the insurance company won't change the registration to themselves, they'll "own" it for too short a period).
If you don't win the bid, you still have the insurance payout to buy another 150.