In real terms, any legal fight starts with you being dissatisfied with the official response of the at fault party/an insurance company. Having been here on a car, and having just guided a friend through it, have a few good comparable (hand over your heart, honest, valid comps) market value comparisons gets you past the 'book value' argument pretty quick. Successful (95% whole) 2x.
My cases involved cars, where book was sub $2000, market over $5000. Something tells me there was state implications (Ohio for me), but I have reports of MI being the same, even being a no-fault state. No, it's no an airplane, but I've read it being used in dwellings and watercraft too.
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For airplanes, forget book value / market value. Your hull insurance is written on a stated value basis. What is written on page one of your policy as aircraft value is what you'll get (less whatever deductible) if you file a hull claim and they declare a total loss. If you do this, now your insurer assumes the right to persue any at-fault party.
If you make a direct claim against the at-fault party (you obviously should) you have the right to claim any / all costs necessary to return the a/c to its pre accident contition.