Following as I'm in the same situation for my wife's car. $4,500+ damage due to being rear-ended, repaired very satisfactorily with OEM bumper cover and floor pan etc but it still shows on on Carfax now.
I took it straight from the collision center to the dealer to get their best offer, which clearly showed a reduction in value of $2,300 due to the accident based on the extent of the repairs. USAA (at fault driver's insurance) sent me a check for $313, even after submitting the offer as my evidence. I have obviously not cashed and am still in the process of going back and forth with them to try to get a more reasonable settlement.
Like the OP, I'm considering using a 3rd party to mediate. Has anyone used WreckCheck or similar for this? They will only take cases estimated at $1,250+, and their online calculator has mine right around $2,000.
At this point, I'm not sure what the downside is to letting them pursue it further since USAA stopped responding.