This is why I get my cars appraised. Granted, it is not an inexpensive process (currently $300 each). The appraiser spent several hours going all over the car (interesting, he never started the engine) and later mailed me two copies of a thick report with all sorts of data on the car, lots of photos, current sales, copies from all of the auto-for-sale books, etc. I took one copy to my insurance agent and had the agent sign and date the other copy as a "receipt." That copy is in my fire-proof (for two hours anyway) safe.
I've never had to wave the appraisal in front of an adjuster but the appraiser told me that he and his people spend a good deal of time in court testifying on behalf of people trying to get fair play. The prices that the appraisers come up with are high, of course. That's their job. It's a number you can use to counter the low-ball offer of the adjuster. Worst case, you have someone available to fight for you.
The insurance company does not work for YOU, advertising to the contrary. They work for their shareholders and their job is to increase the value of the company and to deliver dividends. In an insurance company, one way to do that is to hold down claims. The adjusters know that and they know who signs their paychecks and it isn't you. To get fair play in such a situation, you must have someone who works for you, someone knowledgeable, professional, and not emotionally involved. That person is an appraiser.
YMMV.
Jeremy
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"Buster" in the '95
Our all-Diesel family
1996 E300D (W210) . .338,000 miles
Wife's car
2005 E320 CDI . . 113,000 miles
My car
Santa Rosa population 176,762 (2022)
Total. . . . . . . . . . . . 627,762
"Oh lord won't you buy me a Mercedes Benz."
-- Janis Joplin, October 1, 1970