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Maybe a good idea could be suggesting the integration of the larger quantity of recruits from the Spartan 3 program into the army as potential squad leaders? Specialised (and secret) squads could still exist, but several hundred Spartans could be integrated into the military in the later stages of the war.
It would work very well with the Spartan analogy, since military personnel under the Spartans could become the equivalent of the historical Helots, who served Spartans as foot soldiers in war (and also as servants back home, but that doesn't matter in this context)