stellar evolution - Why do PMS stars on the Hayashi track remain at a constant temperature while they contract?

You are indeed correct. The Hayashi track is one of the surprisingly simple laws in stellar-evolution, where the luminosity is purely dependent on the radius, and not the surface temperature as it remains constant. The reason for this is a bit complicated, but it basically boils down to, as you state, the opacity properties of the hydrogen ion, that becomes especially important for contracting stars with an unusually thin atmosphere, like those on the Hayashi track. Keep in mind that the temperature/luminosity curve is not completely vertical, just very steep.