C.O.B gave you some really good advice.
I'll add that the first thing you need to do is get this gun back together and fuctioning. Then you can worry about having it engraved.
Brad Bachelder can do the whole job for you. He runs a full service shop that specializes in Parker repairs & restorations. If he doesn't have an in-house engraver. He will have his go-to engravers that he sub's work to out of his shop.
Give him a call and discuss your situation with him. He's a great guy that runs a quality first rate operation.
http://mastergunmakers.com/