I recall back when I broke a carbon frame, all it took was a letter from the LBS that it was not repairable and I got the money for a new frame. Can’t you get a nice letter from someone?
As said before see if the LBS will provide a negative assessment to back up your demand…
The insurance company will not care about a LBS assessment, they have their approved carbon repair workshops now (LBS assessment used to be fine, then they moved to dealing with Wheelies etc, now carbon repair)
Just like the car insurance industry.
I suspect the next thing will be market value paid on stolen bikes or total loss. (unless you insure new for old or agreed value)
I am curious as most bike manufacturers warranty would be void after a carbon frame repair. Whereas cars can be repaired at an dealer or approved body shop. It could be worth asking for confirmation in writing of the warranty situation? (from insurance and manufacturer).