Miami drawbridge crashes down on MY Rockstar

What would I do... ???

Get the boat fixed properly whatever the insurance situation...
Simply if insurance plays their games and you get drawn in then they control you.
The important thing in all business and transactions is you maintain control... rule one... period.

In American and Europe it always comes down to the money as to the boat fix issue. Except in Europe liability of the bridge and yacht might be a much different situation and though the bridge might be responsible the yacht may have to foot the bill.
As to Insurance... If you fix the boat while they squabble then it is a simple money claim to scrabble over. And, Court's do well handling that if it comes to it. The owner of the boat fundamentally has a right to enjoy it and protect his interests... and insurance is about that... not about protecting the insurance company interest. Ultimately, fixing the boat needs to be done and the quicker it is the less it will cost overall to everyone. Waiting an playing into the game for the scrabbles with insurers is a loser strategy.

Generally the problem is determining the subrogation of the claim with the insurance. The issue is where that happens at time the claim is made and thereby the insurance is in charge or whether that happens at settlement. Legally in the good old USA it legally and generally happens at time of the payment of the claim. Now if it is a total loss then the insurer basically on payment of claim owns the boat...
The big but is sometimes they have language that caused the claim to effectively subrogate to the insurer during the pendency of the claim until settled so that the insurer is in control "effectively acting as agent/power of attorney for the owner" and the fixed boat is realized back by the own by the completion of the fix. Subrogation means the insurer steps into the shoes of the owner as to the insurance claim... is the owner effectively.

Yes, there can be terms in the insurance that you have to abide or come to terms with them or use their choices... well then you shop elsewhere for insurance or suffer your lumps for being stupid.