[cooper barrett]

IMHO 90K miles on a well maintained F30 is nothing and being driven hard for a week doesn't phase them. If it was stolen by Bueller, that's another story.

I would have pictures and receipts ready but would not volunteer them until the word total is used.

I would get the shop (you are in good graces with) to vouch for the fact that the car was flawless and that it is now not running, driving, or shifting as it did on last service visit. There is a lot of unknown info about this car, mileage since stolen, body damage, and even if there were tires and wheels on the car. *** remember that you control where your car gets repaired.
Just tell the shop manager/ owner that you don't want it back and they will steer the insurance adjuster towards totaling the car. If it was not badly hurt and the wheels are still on it, undamaged with even wear and no abuse signs than you're getting your car back.

The key is to have your shop note, in writing, on paper(estimates and invoices) that becomes part of the file, that they feel the car was seriously compromised and why. If the steering or suspension has been damaged (strut noise, popping or a pull can get expensive quickly. If they drove the wheels off of it, the tires may be down to the belts, the wheels gouged, and the interior and body may need expensive repairs.Your shop can make notes to the effect that implies need to diagnose shifting or engine issues. They may request oil and tranny fluids be tested and failure of the ins. co. to authorize would leave the door open for them to pay future claims.*

You should refer to your state's laws on "Diminished value" as this will appear on CARFAX and other services.
I made State Farm buy back a Benz 320 SLK that was not fixed right (up to Mercedes standards) and found them only wanting to verify proof sources to make decisions. Aristocrat's used car manager wrote a letter stating diminished value. Additionally, letter from Frank Eveland at Eveland Bros. Collision Repair, Inc. stating that the car was compromised beyond proper repair made State Farm offer up an check for almost what was paid for the car along with generous payment for my time away from work and expenses. No bickering whatsoever. I bought my SLK32-AMG with the proceeds.

*Unlike the tranny mentioned above you can make a claim after the fact and most good insurance companies will make good if the claim is plausible to the original claim.