I have the same "-P" on Sea Haven, Hull No. 124.

However, when I registered her after the sale last month, I was lucky enough to have a transferable NY Registration (no title) from the previous owner and I used the HIN minus the "-P" on all the paperwork. Flew right through our DMV.
FWIW, first thing I do when I boat shop, I record the HIN and do what research I can before I go much further. Decoding it, Googling etc. and insuring I won't have DMV issues. When I was shopping and looked at hull no 244 located on the North fork of Long Island, I noticed she DOESN'T have the "-P". But I ended up purchasing 124 with the "-P" and like I said that wasn't on ANY documentation.
I would suggest dropping the "-P" on the paperwork and try again.
BTW, I'm in Mt. Sinai Harbor on the North shore of Long Island. Hull no 244 much to my astonishment was purchased as well and sits in the harbor not far from me. Plus, the son of owner of the Marina who manages my mooring has a 323 he's getting ready for the water as well. Soon, 3 323's will be in the same harbor. Looking to start a local users group. Are you in the NY/NJ/CT tri-state area?
"Sub" Ed