"I don't think the UN can be reformed sufficiently--can't get there from here. It's a council of governments and a giant uberNGO, but it lacks both many of the routine administrative organs of a government, as well as a philosophical basis for acting as a government; it has no legitimacy to expand beyond what it is today."

Well, if you can't reform the UN, you can't make a world government work. I'm not suggesting the UN become a world govt [though some see it as one already].
What I'm suggesting is that once you reformed the UN, and then took on a "test run" one could perhaps use as a template.
So the UN could act as a kind of prototype that will give some idea of how to construct the world govt.

"It was LarryJ, if I recall, who once explained that conservatives object to the UN's authority over the US because American citizens have no voice at the UN--as a council of governments, it's all Senate and no House, so to speak. And that's one issue on which I can clearly see the conservative point of view, and agree with it. I don't want the UN to become the government over me, either. I'd rather start from scratch with the intention of creating a represenative government."

But that is because the UN doesn't work.

LarryJ, conservatives, and people in general like things when they work. They don't have any burning desire to have the UN listen to them opine, rather what they want is for it to function.
A mechanism which makes any organization vaguely intelligent and thereby functional is by "allowing people to have a voice". Ivory towers might be good if you don't want to be distracted [so you can paint pictures or write poetry], but lousy if you want to effectively govern.

"I've mused about what forms of government people might adopt if they had the freedom to colonize lots of planets and set up lots of specialized societies. In that scenario forms such as theocracy aren't so objectionable, because there are alternatives, as long as you protect the right of free emigration. Along the way, though, some of the planets, such as "sector capitols", will have to be more cosmopolitan, and tolerate diversity, in the interests of trade and commerce and government. On those planets, what other form of government would you choose for a heterogenous society, but a clone of the American system? Representative democracy, with institutional chex-n-balances, is the best general-purpose recipe for governing we know, and that's the one we'll reach for in both the space colonization and Earth government scenarios. So I just wouldn't fret about some nightmare global tyranny arising. Relax. It'll be America writ large."

I think you could do better than America and that there are alternatives. But that is something for them to figure out. They would obviously need to look at countries such as America and history in general in order to craft such a govt.
For example, think of Marxism, and the root of evil being property ownership- particularly land ownership. In Space, opposed to on planets, land ownership is fairly meaningless. How does a society which is completely mobile, differ from those land based societies?

And it seems inevitable that space will evolve new technologies and technology is often a driver of political changes.