Thank you for the reply. It's a 2003 BMW M3, coupe, manual transmission. Pre-loss condition was excellent (insurance damage assessor gave it the company's highest condition rating in all areas, "dealer retail"), nearly perfect, with no aftermarket modifications.
One of the tricky things is the transmission option - the automatic was given the name "sequential manual gearbox" (SMG). This leads to a filtering issue on sites like AutoTrader, where even when the "manual" filter is selected, about half the results are actually SMG.
Several times in the last month, I have gone through every "manual" listing in the country on AutoTrader and shared the results. Filtering out outliers, such as very low or high mileage vehicles yields an average listing price of $22,000-24,000 each time I have done this, and doesn't really change with outliers included. Their last offer was for about $16,700.
The insurance company has used a few valuation methods, but regardless of what method is used, if I apply their methodology to the comps I find (e.g. if I use their worst-case rates for mileage/year/whatever adjustment) I always end up in the low-to-mid 20s; I have never seen anything nearly as low as the number they offered, unless I ignore 90+% of listing and cherry-pick pick the two or three cheapest listings in the entire country, in the rust belt/northeast. If instead of adjusting I run some stats on nationwide listings, and use either average or median pricing for my above-average condition loss vehicle, I still arrive in the $21k-24k range depending on search radius and when I run the numbers. I know we tend to overestimate our vehicles' values, but I don't think it's unreasonable to use average or median price for my above-average car.
Subjectively, I am quite familiar with this market, and have been for a few years as an enthusiast. If I could find a car like mine for $17k, I would buy it in a heartbeat. Examples like mine usually go for low-20s in both my own experience and in the experience of my appraiser (an expert in and broker of more rare BMW models). It's not uncommon to see really excellent examples (like mine but much lower mileage), in the mid 30s.
Not that it's the ultimate authority or anything, but Hagerty lists the value for a "good" 2003 M3 at $22k and "excellent" at $34.5k today, so I don't think I'm too far off in my understanding of the market. I am absolutely open to changing my position if I'm shown even moderate evidence, but all I've seen to this point overwhelmingly points to the reasonableness of my expected settlement.
I will upload a spreadsheet shortly with literally every manual coupe nationwide on AutoTrader recently.