Chad,
Welcome to the forum. Unfortunately, our members outside the U.S. are unaware that a vintage motorcycle can be found on the curb in any given week and in any given neighborhood here. Yes, it is April 1st.
I don't know of BSA engine builders in NY or PA or closeby there. There are two comercial shops I would look into outside your immediate area. First is "Morrie's Place" in Richmond, IL.
http://morriesplacecycle.com/services.html Talk to Ed Zender, the Owner. If you have watched
Cafe' Racer on Velocity TV you may know of them by the Norton they built for the show. I know Ed by swap meets and having been to the shop. His knowledge and shop are impressive. The second is Wes Scott from Ft. Lauderdale, FL.
http://wesscottcycles.com/ Wes rebuilt my wheels and did a great job. In talking to him on the phone, I got nothing other than the impression of someone I would trust with an engine. Of course, you must come to your own conclusions regarding what you think of people, personally or professionally. I suppose there are more out there to trust, but I don't know them first hand. One I definitely would not use is also located in the south. I could provide that name and the reasons why outside the open forum. If you want to know, drop me a personal message.
As to my being in western NY, I might get there frequently if my daughter gets accepted to Ithaca or Syracuse.
Regards,
Richard L.