Spartiatoi take 1 turn to train as all other infantry do. They do require the highest level of barracks though which takes some time to get to.

And Quintus I'm surprised by your experience with Thessalians. They have good stamina, the same as Molosson Agema, better than Hetairoi. Sure they're not Prodromoi in terms of stamina but they are the same as Lonchophoroi and are better chargers.