I remember very vividly a '69 GTX that ran out of Fountain Avenue in Brooklyn during the late 70's, and it had a big PLYMOUTH sticker on the quarter panel ends. This was very common with local small budgeted racers, street or track.
If a dealership were ever involved, their showroom/parts department addresses would have been crested on either the doors or quarter panels. I suspect your Bird was from a local racer which as someone said, there were thousands here on Long Island.
If he or she were street racers, I'm sure they would have been NO/TIME testing at any of the local tracks and that in itself is a nightmare to try and find within a sea of photographs that cover the main NY tracks.
A similar account took affect with a NY based HEMI Dart that is now in the hands of a racer on FABO and was raced at NY National. He has pictures (very blurry mind you) but we weren't having any luck at all to find the speed shop that sponsored it. I got real close, but the gent passed that ran the speed shop.
Talking of speed shops, S&K Speed which still operates out there may have a clue. S&S Speed in Brooklyn also sponsored some cars. Looking on their websites might bring up a clue or in this case "A smoking tire"
This could have very well been a NYC based car that ran out on the Island.
Good luck.