The power of the Spartans is their infantry. Besides using Champions or Skiritai you can also mass up skirmishers and combine them with the Brasidas hero and some melee units, or you can go for a large number of hoplites which you boost with the hoplite tradition technology and the Leonidas hero. As infantry is slow think about using some ranged cavalry as well.
Actually, rushing with the champions shouldnt work so well. They are so expensive, the enemy could easily create a big citizen soldier army which should be able to overwhelm them. At least thats what I estimate.