If you have the liquid cash available, and you know for a fact that the other has high enough policy limits (I'd imagine they do). Nothing stops you from paying out of pocket for the repairs yourself at a shop you choose and then submitting it to their insurance. If fault is clear (sounds like it), you will have a tangible dollar amount (loss) that their insured caused you that they will have to cover. It may take a while to get repaid with this kind of hardball stunt, but it would get the car repaired.


This won't work if you take it thru your insurance company as you are bound by the procedures set forth in YOUR policy.

<edit>
Looks like you may be in NY? If so, small claims court may cover 5900 (says 10K max). You'd have to pay to get the car fixed (have to have monetary damages) but then could file yourself in small claims court. As soon as the person who hit you gets served papers and if his policy limit was high enough you'll soon have a check.

https://www.nycourts.gov/COURTS/nyc/.../general.shtml