I saw an article for special features of 64.5 Mustangs in the "links" of MCA that said Ford used a fixed passenger seat until May 8, 1964 then put a sliding track on the passenger seat.
My 64.5 convertible built on May 12, 1964 has the sliding passenger seat!
The only "problem" is that your car was very likely not built on May 12th.
Guessing that the date came from the door tag and that is only the date that that plant estimated (read guessed
that it might be finished on sometime in the future as it was assigned when the order arrived at the plant not when the car was completed. We often refer to the door tag date as the "projected build" date for this reason.
From other examples we know that date could be off by up to three weeks (earlier or later) so your car could fit into the pre - May 8th range with ease IMHO