Here are some preliminary results for Cyprus. If you think they look promising I will delve into libraries to get details.
1. In the Late Bronze Age (LBA), also know as Late Cypriot I,II, and II (generally dated from 1600 to 1175 b.C.) Cyprus was a palace-based kingdom centered on the citadel of Enkomi (south-west of present-day Salamis) and based on the lucrative trade in copper which was mined in the Troodos foothills. Around 1175 b.C. most of the main settlements were destroyed, possibly by the elusive ‘Sea Peoples’.
Here is a map with the main settlements in LBA Cyprus:

2. Cyprus was wealthy, powerful and influential in the LBA, as had always been suspected by scholars on the basis of the ‘Tell el-Amarna letters’ found in Egypt. These letters are diplomatic in content and indicate mutual respect and friendship between the rulers of Egypt and those of ‘Aleshiya’. Recent petrographic analysis has proven beyond doubt that Cyprus and Aleshiya are identical. The provenance of the cuneiform ‘Amarna letters’ is either Kalavasos or Alassa, both on Cyprus. Other major settlements on the island were also located near the copper sources and smelting workshops: Kition (Larnaka), Kouklia (Palaeopaphos), Hala Sultan Tekke (near Larnaka), etcetera.
3. From ca. 4000 b.C. on Cyprus furnished copper to the entire Mediterranean world. The Old Testament ‘Isles of Chittim’ are a reference to Kition, along with Tamassus the best known copper trading station at the time. Cypriotic copper has been found in the Levant, North Syria, Assyria, Egypt, Ugarit, the Palestine, Rhodes, Melos, Thera and Crete, and in return large amounts of goods from those regions have been found on Cyprus, probably as a result of their exchange against copper.
Amarna-letter EA40 from the Minister of Cyprus to the Minister of Egypt:
My brother, to Sumitti I have sent
nine talents of copper, two elephant tusks,
one shipload of wood;
but he has given
me nothing. So send thou now
ivory, my brother.
Now, as a present for thee, I have sent
five talents of copper, three talents of good copper,
one elephant tusk, one piece of box-wood,
and one shipload of wood.
After 1400 b.C. enormous amounts of Mycenaean pottery were used on Cyprus, but the idea that this was the result of Mycenaean settlement or conquest have been discarded because no other significant remnants of Mycenaean settlement during LBA have been found anywhere on the island.
4. Cypriotic copper was melted into oxhide ingots of ca. 10 kilogram that were used as an international monetary unit throughout the Eastern Mediterrranean in the LBA. You might consider using them as the currency unit in the mod.
Picture of ingot:

5. Information on LBA Cypriotic military affairs is scant. However, this much is sure:
-- The island had its own fleet
-- Cypriot LBA settlements were (re)built on a rectangular grid plan: a series of parallel east-west avenues and a perpendicular main street. Most cities were walled. Enkomi was a citadel of ca. 400 by 350 metres enclosed by massive walls (as ‘Cyclopean’ as those of Mycene, according to one archaeologist) with square towers at regular distances and four gates. The gates in Cypriotic city-walls corresponded to the grid axes and had grand buildings along the main streets. Official buildings were embellished by ‘ashlar’: finely cut stone blocks on the facades. Sanctuaries contained ashlar-finished horned altars harking back to Minoan times.
LBA horned altar:

-- Cypriot warriors wore small round shields and horned helmets, little or no body armour, and bore spears with wide-bladed spear-heads which, in the older literature, are often mistaken for ‘swords’. Statuettes of Cypriotic gods are without a doubt antropomorphous and can be taken as exemplary for a warrior’s equipment:
LBA Statuette of bearded god:
Cypriot spearheads:

-- Around 1200 b.C. they also began to bear swords. There have been 9 finds of the so-called Naue Type II sword or ‘raider-sword’ of Mycenaean origin, and Cyprus’ position as a main trading partner of the Mycenaean mainland makes it probable that these were in use by Cypriotic noblemen around 1200.
Naue Type II sword

-- The Cypriots had chariots. In Amarna letter EA35 the Cypriot king writes to his ‘brother’ the king of Ugarit:
Speak to the King of Egypt, my brother. Thus says the King of Alashiya, your brother: All goes well with me. With my houses, my wife, my sons, my chief men, my horses, my chariots, and in my lands, it is well. And with my brother may it be well. With your houses, your wives, your sons, your chief men, your horses, your chariots, and in your lands, may it be very well.
The gradual appropriation of Mycenaean customs makes it probable that Cypriotic charioteers rode in couples, of which the main warrior bore spears and bows.
Four-horse chariots appeared on Cyprus only in the Iron Age, i.e. after 1000 b.C.
-- Names of prominent Cypriots of the period as far as we can reconstruct them from the sporadic sources: Pastumme, Kunea, Etilluna, Usbarra, Belsamma.
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