>> No one outside the Pentagon got to listen to most of these recordings until decades later
Ya, total bunk. There was/is a multinational intelligence sharing community. Certainly the "five eyes" nations would have acces. Heck, the UK and Canadian waters of the north Atlantic where the most interesting place for watching Russian subs.
But were they given access to the raw data, or reports?
I would bet that nobody had the raw data. There would have been too much of it to record and move using the tech of the time. The system probably created contact reports, little more than a pointer and a timestamp, at local stations and shared those electronically with a central database for triangulation.