I went through this hell last summer. What I can tell you is get every piece of supporting documentation available and have it ready they asked me for all receipts. They look at everything when adjuster inspects the vehicle. I also scrolled through all car sites looking for comparables my issue was it was a unique car and was difficult finding comps since mine was such low mileage and pristine. Gather all you can as well as KBB stuff and they should also provide you their report which you can also negotiate from, I'm not gonna lie this won't be fun but good things are your family is ok and you've done work before so now your a pro on the second one when you find it

Just be ready to support your argument and you will be fine. I held to my guns and got a very good price and do not keep the car I did and ended up with a bunch of parts I never sold and then couldn't find anyone to take the carcass as there wasn't much meat on bone left.