Not everyone is trying to screw you. Give him a $ number for the replacement which is fairly easy to calculate and a short deadline to cut you a check before you will need to file a police and insurance report. If the police report and insurance report is delayed a week (worst case) it is still valid as you have the video and tracked down the owner. Most business owners know that if they are at fault, caught on video, and then try to not cover the costs it will come back to bite them one way or another. Just make certain you have the right total cost.
I am with Roz on his approach consistent with me hitting the "like" button. What I will add is that I would be firm on the few days that you are requiring them to pay. I could be wrong; but it seems like you could use the
lever of being able to file a criminal complaint to make sure they hurry up the proper amount! Keep in mind it was a "hit & run" which should make it more than just a "civil offense" Since the evidence is so clear ... if it did come into "small claims" along with an eventual police report & filing ... it would tend to be a "slam dunk" IMHO.
From actual experience ... some officers handle these events differently. I know one time an officer said he would not help track down the offender in the future ... if I personally was not willing to file the more serious "hit & run" formal complaint! Other instances the officer said I don't need to part of showing up in court or filing an affidavit ..... he would do the "criminal hit & run charge" without me. Another situation had a more forgiving officer who said to get back to him if the "careless driver" did not properly pay up with "fair compensation" that the small business owner requested. Like Earl possibly alluded to "your specific town or city" might be a factor on how you proceed.
As far as Randy's "evidence of laughter" it seems like "Marsy's Law in some states might also come into the picture. I know we had graffiti happen to a just painted $8,000 exterior paint job & it was right after Marsy's Law was passed in our State of ND. I was shocked that the officer that responded ... insisted that I & the "also affected" neighboring business ... fill out the Marsy's Law Form for "VICTIM DAMAGE".