A thalassocracy is more how we project that power, rather than the government itself. Moreover, I think we ought to very much avoid slaves in the army as combatants; just need to look at the janissaries to see how that works.
Anyway, to expand on the proposal I had earlier for the government:
Hadeaen League Reforms:With the war against the hive, the structure of the league is in need of dire reform into something far more resilient and stable. Mimicking the other realms of the known world for the most part with the establishment of a monarchy to serve as the ruler of the league. In practice regarding the king's power and succession we differ vastly. While the ruling dynast is expected to have children, the successor to the monarch is choice via the council, made up of the rulers of the city states. In order to prevent consolidation of one city state over the others, no member of the council, nor their families (Barring the monarch's) are eligible to be voted for the position on monarch. The eligibility for candidacy is simple; any noble not barred from being king by either being a council member, or being related to them, is able to be elected as king.
The powers of the king are vast, but unlike our contemporaries, are tempered by the council. Any laws or proposals need to be accepted by a 2/3rds majority, with each councillor having one vote and the king having two votes. While the royal vote superiority is apparent, the control of the council over who succeeds the king is considered to be an effective deterrent against abuse; the king cannot expect to have his heir inherit the throne if the council is unhappy. The council, for the most part, is effectively untouched in how it's members are selected; the member cities are effectively given autonomy on how they govern such internal affairs.
The military however is to be unified under royal command, and as a deterrent against individual city-state loyalties, will be mixed and melded: The army now serves the league and only the league. The member states are allowed to raise levies for their own use no larger than half of what they provide to the League.
Legally, the council is the highest court of law in the archipelago, and any disputes between member states are arbitrated and ruled upon by the council, with the disputing councillors being excused from voting on the verdict.
Design
Standing army: (2) Jilladilla, Taricus
Freedom for Service (1) Tack
Government:
This thing (1) Tack
Hadean League Reforms: (1) Taricus