A 57 ford from NY would not have had a title, I think the info you have on 73 and up is correct.
NY registrations that can be transfered will have a space on the back to transfer the vehicle to the new owner, later titled cars have registrations marked non transferable.
You wil never get NY to issue a title for the car as they never had one.
The old signed registration and a written and signed bill of sale is all that would be required in NY.
Try again in FLA and if you are lucky you may get someone in DMV that knows what they are talking about.
Also search the NY DMV web site, I remember seeing title vs year info there