I think the idea is more along the lines of:
"The Q aren't a species, they're a designation for a category of nigh-omnipotent entity, and the Q Continuum isn't a specific, single nation that has rival or subordinate groups, it's an overarching entity that includes and represents ALL such beings."
There are fairly plausible ways for that to be a stable phenomenon. Say, as each species develops towards godhood, it is contacted by and integrated into the Q Continuum, with good reason. Coordinating between the members of the Continuum decreases the risk of conflict, and the old differences of physiology and spatial location those species may have had before they ascended probably matter a lot less to them now than they did before. So a group like the Organians may well be both a subset of the Q Continuum and their own independent entity, a species of powerful beings that simply prefer to live on their own planet and recreate a peaceful, low-technology lifestyle.
But thing is all inhabitants of the continuum are Q, so... it really doesn't seem to fit. it is, at worse, a cheap solution.
So, speaking of subsets of the Q, they'd still be Q, nothing more, nothing less.
Actually no, Trelane only appeared once. Literally every time Roddenberry 'needed' a new species of nigh-omnipotent advanced energy beings, he made up an entirely new set. That's one of the reasons we have this problem in the first place.
He appeared at least twice, in the latter one his parent's showed up and gave him a time out.
If you don't believe me, I will link the episodes summaries.
(thrice if you count the Judgment Rites game)
Conversely, merging some of the entities into a single community whose members do as they wish (that is, the Q Continuum) tends to make this easier, because it means you no longer have to worry so much about the question "but if they seek regular contact with the Organians, why not with the Metrons, the Thasians, etc.?)
And that comes with the price of making the universe smaller and neater. nice for writers, less so for a series that was, in part, about exploring the unknown.
I'd rather have a wide galaxy, teeming with life and the unknown than a neatly defined Continuum.
It is more strenuous on the writing team, but then again, Star Trek has muddled its continuity time and again (most notably the Scotty TNG episode AND the Generations movie) without any extra complexity.
Plus, it has never been stated, on screen, that the Organians, Metrons and what not were part of the continuum, and has been made no mention to them from TNG onward, that I know of.
