Granted that would be a very thematic idea, I do like it honestly. But lets have a little brainstorm and put some more ideas into circulation?
(Side note; honestly I am a nerd and spot references like that all the time, to normal people ya they wouldn't catch it so it was a little brash to just jump out there and use it.)
Midnight, we can't base this off staff using the names. The names of staff are that of the Greek(and to some extent even Roman, I would say circa just after the formation of the Romans) Gods/Dimi-gods names. So disclueding them we have to turn to weapons, armor, guns, bombs. Now for a bit of a small nitpick of my own really and this is more aimed at OOO, not bad but just a point. Some of the armor/swords look like that of the pre & post Roman Military. As the Greeks tended to be more Bronze over steel, where the Romans where more steal and leather with Steel padding and the starting of some forms of chain-mail (though they never really had chain-mail it was more along the lines of layers of thick leather and riveted steal.) Now the might have had Coif under their armor, but for the most part if they needed some kinda metal plating it was steel (Mostly for the wealthy) and Bronze (Common soldiers).
That being said, you do have some nice ideas, but I see it more like this: The Morai would be the Spartans, and the Spirals would be more along the lines of Athenians. Morai seem to be more war like and tend to put more time and money into their war machines/gear/weapons. Whereas the Spirals seem to be more well rounded and have the extra edge when it comes to inventions, schooling, ETC. Over all I would wager that Spirals are in a since 'smarter' then the Morai, where the Morai are more 'war prone' when it comes to innovations. Not disclueding civilians at all, they might have more along the lines of what we would call 'the basic designs of life'. A working home, jobs, income, ETC, however when it comes to where Tax money or just plain out Spoils of war funds go, I would say that is more spent on military when anything else.