You'd want to check out the Osprey book "Bronze Age Greek Warrior" (http://www.ospreypublishing.com/store/Bronze-Age-Greek-Warrior-1600%E2%80%931100-BC_9781849081955) Even though I am almost certain the author is the same as the website I noted - a lot of artwork and hypotheses and even text are the exact same.
I was going to first say I agree with you on the Shardana horned helmet not being included, until I realized like the Peleset feathered tiara the horned helmet is apparently ubiqutous in the Aegean area.
Greek Age of Bronze (GAB for ease) notes the eras of helmets from the Mycenaeans:
Early (2000-1500): http://www.salimbeti.com/micenei/images/elmi9.jpg
Middle ( 1500-1300): http://www.salimbeti.com/micenei/images/elmi10.jpg
Late (1300 - 1100): http://www.salimbeti.com/micenei/images/elmi11.jpg
I think the Early is out of the question but I have seen Middle Era helmets depicted in Late era stuff (Easily by the same author as this website), after all we do still hear of boar tusk helmets in the Iliad (even though one is already depicted in the Late era helmets). Here's a specific Iliad reference (Book 13 circa 700): "Pisander hacked the horn of the horsehair-crested helmet right at its ridge, lunging at Menelaus.."
It seems the GAB author considers 'tubes' to refer to a horn (judging from Achilles' later helmet having four tubes, and then GAB author noting the new helmet with 4 horns). Either way I do think horned helmets aren't going to be anachronistic or unhistorical - too late for me to look for specific period depictions of them but I am basically 100% certain they are authentic. Maybe just for the Akhaioi, but I don't see a reason why Trojans wouldn't use them too.
Thracians: I found it interesting how at least in my book's translation Thracians and Phrygians are called horsemen. Could easily just mean charioteer, Hektor's the breaker of horses after all but it makes me wonder if you can't cast the Thraco-Phrygians as riders of horses and not chariots. There's no sort of consensus on riding horses in this period but I'd favor a middle of the road opinion - I don't agree with the idea that nobody rode them in the area (whether for travel or possibly for war), but I don't imagine it was very common. Either way, you could consider it for them.
One reference I did come across that's interesting is Book 13, #670: Heleneus charged deipyrus, cleft the side of his head with a massive Thracian sword". I don't think there's any way that's a falx, since we don't see anything approaching a falx until maybe the 5th century. But if there are massive European swords of this period it might fit the bill. Otherwise what I would recommend since you've got a clean slate of not having worked on prior materials or designs for them would be to go with that kind of "Barbarian European/Balkan Bronze Age" Vibe, like Illyrans or Thracians but with Bronze age aesthetics
1) Thracians & Phrygians (who are basically Asian Thracians right now) are noted horsemen. Rhesus has great horses for his chariot. So does Asius son of Hyrtacus. Whether or not you can get a chariot script you could have them have horsemen.
2) I seem to recall the Thracians being noted as numberless hordes in Rhesus contingent. So that might support a horde of "Peltasts". I am not sure I'd do peltes, but more likely round shields of wicker and hide.
3) Top dog Thracians can fight and look like Trojans/Greeks
Locrians: Book 13, #620: "But no Locrians followed the hearty Little jaax. They had no love for stand and fight encounters- h ad no crested bronze helmets to guard their heads, no balanced shields in their grasp, no ashen spears, only their bows and slings of springy, twisted wool. Trusting these, they followed their chief to troy, shooting with these, salvo on pelting salvo, they tore the Trojan battle line to pieces. So the men in heavy armor fought at the front, they grappled Trojans and Hektor helmed n bronze while Locrians slung from the rear, safe, out of range.."
I tend to follow a liberal interpretation of the facts so I do imagine they could have had light spearmen, but I think since this is the only instance of the Akhaioi for an ethnic group singled out in fighting style (I don't think the Myrmidons are singled out so, just cast as best of the best but otherwise they presumably fight like the rest) it rings true.
But I think it shows the majority of Locrian troops would be light slingers, archers, and maybe javelineers. A small core of high end troops being spearmen armed like Little Ajax.
Just to repeat the research I found for organization of politics and military:
(W)Anax = "High King", Agamemnon and Priamos get the title the most. Sarpedon, Nestor and Diomedes apparently here and there have it given to them.
Lawagetai is the "marshall", the guy who commands the army.
Nobility titles are horribly complicated. I'd go with Basilieus (or the archaic, Linear B version of that) for kings like Odysseus or Nestor or Diomedes or Greater Ajax, since I've heard its the term Homer uses and can be translated to Chieftain/King/Lord but not as lofty as Anax.
If all the Greeks have some sort of connection/union under Agamemnon (whether they can still war with one another or not), you could reserve Anax for Agamemnon. Otherwise it seems like in real history Mycenae didn't have that kind of total authority. I recall the major Mycenaean palace-kingdoms in history as being Mycenaea, Thebes, Pylos, Crete, and another I forget the name of. You might want to reserve Anax then for the major Kings - Agamemnon, Idomeneus, Nestor, Diomedes, and possibly Thersander of Thebes (If set right when the Trojan War starts, since he dies before the Iliad). Thersander only earns it for a historical context rather than myth, since his 50 ships are matched by others while Agamemnon/Idomeneus/Nestor/Diomedes all contribute the greatest number of ships (100, 80, 90, and 80 I think).
Eqeta/Equeta is the "Knightly" caste of the Mycenaeans, what I read to be the retinue of the king. Some argued that folks like Odysseus and Idomenes (Cretan guy) are the "Equeta" of Agamemnon, but I tended to view them as the retinue of a Basilieus rather than a Basilieus itself. Since you're going with individual Greek kingdoms rather than just "The Akhaioi" under Agamemnon, I would reserve Equeta for a troop title and find another term for lords beneath Agamemnon or Odysseus or Idomenes or Achilles.
Promachos was just a term I remember coming across, I am not sure it had any official bearing but it translated to Champion/fighter at the front. I forget what the reference was, I think it was the Osprey Mycenaean Book (not quite as good as the Bronze Age Greek book in my experience) saying that title could be afforded to the 'light' infantry who fought with swords rather than spear. Either way, you could use it to refer to those "once mentioned" Heroes of the Iliad who might be greater than an Equeta, but not high enough to be a lord.
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On the topic of Luwians, I tried to develop my own lexicon for them based on authentic (at least from what I could access on google books and such) Luwian terminology, since we don't really know what their military was like or organized or termed. If you want I can PM you what I have, though I'd warn it's very messy and there's a healthy degree of creative licensing. It's not terminology like "Spearman", but more a term for the tier. "Hastali/a" translated to hero or champion, so I gave it to tier 5, "Arawani" (or variations of it) meant "Free" or even "aristocratic", so I appropriated it to refer to a noble warrior the same way "Azat" in armenian means Free and Noble (and you find that feature elsewhere in other languages).