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The thing about this car is that it's a Y84 ie, bandit edition with a 4 speed. It's right on the cowl plate. I've already been looking around, and you just can't find them. I don't want an automatic.
I had this issue ~15 years ago with a rare Audi (V8 5 speed). The insurance didn't want to pay for the car but about 1/3 the actual market value like an normal cruiser automatic. I went to an auto auction a few days after the accident and kicked some tires and bought a cheap 10 year old Passat to use until I got the settlement and replacement car; kept me from feeling pressured to settle. I just kept refusing to agree to their valuation and provided like-cars for sale and completed sales showing the real market value. Eventually when the storage bill got high enough, a manager stepped in and looked at the documentation and I had a check for the fair value in a few days.
But until it dragged out and ran up their bill and time, no one would step in and look at the case (this was Geico).
So your strategy is what andyd said above, get comparables for similar 4spds, and let them stew on the storage fees until they make it right.