Thanks for the link. This is a large part of what I was looking for.
I imagine with Klingon politics how they are that houses are constantly shifting round in terms of power and influence. There are probably plenty of fledgling houses that rise up due to, for example, a warrior distinguishing themselves and attaining high rank but then only last a couple generations before falling again whilst the older houses that have been playing politics longer tend to retain their power and influence unless something really bad happens to dishonor them all.
That's my impression as well, which is why I found it curious that the house of Mogh could compete so long at such a high level, despite it basically being built up out of nothing (since all their old holdings must have already been forfeited in the past - unless they were kept by the Chancellor rather than absorbed into other houses, so that Gowron would be able to return them?), and with Worf not even active in Klingon politics.
I definitely think the house of Mogh was more than just Worf and Kurn. At the very least, wouldn't Alexander have been in that?
Officially maybe, but then again, maybe not. He lived on Earth with his human grandparents, very actively not being Klingon. By the time he had any interaction with Klingons again, the House of Mogh had been disbanded again and he made a specific point of saying he had no house, and of avoiding even calling himself 'son of Worf'.