Very interesting site, thank you.
where individual houses all controlled pieces of the military
In Reunification, Vulcan apparently had their own indigenous military force. Dominion war Betazed had something too. When there is references to "Klingon houses," I think of something like the family houses, or noble houses in Frank Herbert's Dune novel series, where a major house would control an entire planet, or multiple planets. If a Federation world could possess a military, why not a (planetary) Klingon house?
We counted black people as 3/5ths a vote here in the US at the time of our founding
For purposes of the apportionment the (white) members of the United States House of Representatives from slave states. Non-slave blacks in the north were counted (like whites) as whole persons. Once slavery ended all blacks and whites were counted as whole persons. This was done solely to deprive slave states of power in government.
The number of individuals in each Federation memberworld could very wildly.
Maybe. Or maybe the Federation requires that a potential Member State to have a population within a certain range.
Perhaps, or you could have a number of planets whose individual planetary population fall below the minimum requisite numbers , but whose populations wanted direct representation on the Federation council.
Some council seats might represent a pool of dozens of different species homeworlds, whose collective population meets or exceeds the required number. A composite body. In some cases, as their populations grew, the "states" would divide into smaller numbers of planets until ultimately each species possessed their own council seat.
This way too, you could increase the Federation's size and statue by incorporating bodies like Graves World into the Federation, even though it only has one resident.
How this would jib with Picard telling Lily of the over one hundred and fifty planets in the Federation, I don't know. Of course he did say "over."
adopt some variant of liberal democracy
Klingons in general hate democracy
The Klingon (or Klingons) representative on the council would practice democracy in that venue, that doesn't mean that the Klingon planets would abandon their noble born aristocracies.
..it's what you do to your neighbors that counts...
Ideally, I think Federation law covers the protection of all its citizens (and even non-citizens) on every member world.
Something like murder laws in America, the Federal gov. has no general law against it (only special cases), the States have murder covered. The Federation enforces it's members laws, and has few of it's own.
...(ritual combat is still allowed on Vulcan, for instance, and arranged marriages are allowable).
I think such instances are more private affairs than government-sanctioned ones.
In the case of Vulcan, there is likely a general law against murders. However there would be a specific exception for Pon Farr combat on the books, a religious consideration or something.
The appeal of membership appears to be that you are now part of a community that can and will come to your aid--economically, politically, socially, militarily--if you ever really need it.
You don't need to like (or approve of) the folks in your alliance, but it good to have those allies.