In all likelihood the NY GOP would be too liberal for you and you'd win the Conservative nomination with a GOP/C split. I'd say 15% in that case with your strongest numbers on Catholic parts of LI, Staten Island, and a few isolated parts of upstate NY.
Thats a well thought out scenario, but I think he'd do very poor across Long Island/Staten Island, including the Catholic parts (better than the rest of NYC but still poor) because of issues like gun control. He would do best in upstate counties excluding populated places like Erie/Monroe/Onandoga/Capital District. He might even win that awful Hamilton County.