If you can convince me that Meyer or Bennett knew what a Franz Joseph Technical Manual was I'll eat my hat.There was never a Klingon neutral zone in TOS, the idea there was one probably arose from the Franz Joseph Technical Manual where an “Organian Treaty Zone” appears that’s essentially the same as the Romulan one. Although, there was some speculation back in the day that part of the Kobayashi Maru test’s surprise was being attacked by Klingons inside of Romulan territory.
What I suspect that they did know was that there was a Neutral Zone near Gamma Hydra. And that "Klingons" made more sense to a general audience than "Romulans" and that they had stock footage of Klingon ships and they were not going to explain The Enterprise Incident or why Romulans would be using Klingon ships.
So we get a Klingon neutral zone. And again in Star Trek VI.