One account by Pausanias (the one from Anatolia, in his 'Description of Greece') mentioned that the Spartans had a chained statue of Ares just outside the city, with the idea being that the martial spirit and victory were never to leave Sparta. He also mentioned something about the sacrificing of puppies to Ares. So the Spartans like him, even if nobody else did =P
And a mention by the poet Tyrtaeus (lived in Sparta, but no real consensus on his origin, possibly from Laconia): "I am a squire of the lord of war, Enyalius (byname for Ares in Sparta), and I understand the lovely gift of the Muses."
We do have some archaeological remains of religious beliefs and practices from the Spartans themselves, but IIRC, it's mostly remnants from the worship of Artemis-Orthia.
Your point still stands though. Tis a pity that even the perioeci didn't bother to record the culture of Sparta and Laconia, since the Spartiates themselves obviously wouldn't.