I used to deal with this A LOT at my old place. Honestly this guy sounds like one of those "difficult" customers, and i base that off of him not wanting to pony up a few hundred to get things working properly. I would bill him, but be prepared for resistance, then offer to half it (or discount). That was our go to for these types. It will end up costing you more in time trying to get the whole bill, Halfing or discounting makes the customer feel like they are winning after you invoice the entire bill. The stories i could tell about these types.......
It comes down to this, how much is it going to cost you to collect?