It’s pretty tough, but you need an expert appraisal that takes into account the accident. Costs usually a few hundred dollars. You submit the appraisal to the third party insurance company and demand payment. Michigan is a no fault state so it might be difficult, but I’m sure it’s possible.
My sister got about $7k in diminished value, and I was able to get around $5k for my mom. My sister’s claim was in WA, and my mom was in OR. It only works if the car is fairly new. If your car already has high mileage or many years of use, then an accident isn’t going to diminish the value by much—if any.
I've never tried myself, but I have anecdotal evidence that suggests it's difficult/impossible in Michigan, which is why I'm curious to hear from someone who's actually had a claim paid out. Even in states with diminished value laws, it also looks like it's difficult. A quick google search and the first few pages of results are almost exclusively law firms.
When it isn't your fault, it is not difficult. Even if your dealer will not give you the " we'd give you X for clean, but with a new motor, we can only give you x-y" in writing.
If you take the dealer's written offer, then get a "black book" trade-in price (the blue book is not the gold standard for dealers, the black book is).
Then I would print out 3-5 raptors that are for sale with comparable mileage and options from AutoTrader, or someplace else.
Industry standard target for profit on trade-in vehicles is approx $1800. So in all honesty, if black book trade-in +$1800 is the same price as the average listing price for comparable raptors in your state, you will have a difficult time being compensated.
If you have mechanical coverage on your car insurance, this entire process becomes WAY easier, BUT, being that this was no fault of your own, even without mechanical coverage, you still have a chance at negotiating with ford/the dealer to seek compensation.
I've done this successfully in Tennessee, Louisiana, and Pennsylvania over the past 20 years. (about once every 7 years I seem to have the unfortunate luck of being hit by another driver in an almost brand new vehicle. the last time it happened, I hadn't even made a payment on the truck yet and was rear-ended by a drunk.)