Here are some suggestions and remarks to try to improve and make more realistic the Lacedaemonians:
I'm sorry for my bad English
-In test version 2.55 of Rome at War, there are 2 mora: that of Amyklon and that of Geronthron but the mora of Sparta disappeared after the Battle of Leuctra and all the laconian hoplites adopted the lambda after that.
-In 300 BC, there remained about 1000 homoioi, the others had lost their title either in combat by cowardice (tresantes) or by poverty (impossibility of paying their ecot to the syssitia), they became hypomeiones and there were many more than homoioi.
There is the conspiracy of Cinadon which is an example of the numerical superiority of hypomeiones against the homoioi. When a man denounces the conspiracy on the agora there were 4000 men, only 40 were peers (1 king, some homoioi, a few gerontes and the ephors).Maybe adding them will not be a bad idea.
-The skirites are too weak. In the Spartan army the skirites formed an elite corps of light infantry. It is known that in some Battle like that of Mantinea (418 BC), they were 600 on the battlefield and they fought on the extreme-left wing in the battle-line, the most threatening position for the hoplite phalanx, they can also be used like scout and walk in front of the king.
-Shields and helmets :
1) Homoioi have just pilos helmet in the game but they also had chalcidian helmets at this period.
2) For lochagos you can add chalcidian and pilos helmet with lateral crest.
3) The lochagos have the shield of the king in their equipment (red solar) perhaps you could put it to Areus and Cleonymus.
In their equipment I noticed that you put the shield of the Talthybidae clan,
if you ever want to replace the royal shield (red solar), you can put these 2 shield episema of the families of sparta: the first with the 2 snakes is the episema of the Melabontidae clan.
The second episema is the drakon, shield emblem of Aegiades clan.
4) Also add more shield with lambda as for example: a red shield with a white lambda or a white shield with a red lambda...