I agree that you should immediately consult with an experienced local attorney. It seems like you have a decision to make -pay wht they are asking or risk arrest. If you decide to pay it, I would suggest that you retain counsel to assist to be sure that no charges will be filed. Even if you pay it, technically they still can charge you so you should proceed with caution.
Ellis Klein, Esquire
I agree completely with everything that has been said thus far by Attorneys Keller and Klein. You need to retain a good attorney regardless of what decision you make with respect to the choice that has been presented to you. Whether the stated costs of installing a new door is unreasonable or not would require an examination of the door by a skilled installer, but paying the requested amount may be better than the alternative. With no offense intended, I question the reliability of your opinion about the extent of damage, unless you have had an opportunity since the incident to examine the door and attendant damage closely in the light of day and without the distortions of alcohol. Since I haven't seen it, I really can't agree or disagree with your assessment of the likely cost of a comparable replacement door or whether the present door is repairable. The labor charge for installation of a new door seems clearly excessive to me unless there was substantial damage done to the surrounding framing. In any event you need counsel to assist you in "settling" the matter. As Attorney Klein has stated, paying the money under these circumstances does not prevent the filing of criminal charges. Promises by police officers are worth the paper they aren't written on. Binding promises come only from a Commonwealth attorney. If charged with Criminal Mischief the offense looks like a Misdemeanor 1, but I could envision charges more serious than that being filed as well. Secure counsel before you do anything.