It's Time to Engineer the Sky: Global warming is so rampant that some scientists say we should begin altering the stratosphere to block sunlight, even if it jeopardizes rain and crops | SciAm

You are passing a lot of assumptions as facts here.

But the problem is: the world won’t stop polluting, won’t stop growing its economies, won’t stop expanding.

Unless you are a time traveler, this is a belief, not a fact.

Even if the US and Europe cut their emissions and slow down, the developing world, India and China and Nigeria and Kenya, and so on, won’t. They see the standard of living in the West, they think their people deserve to live just as well, and they see we got there through unchecked resource consumption within a capitalist economic system, and how the hell do we have the right to tell those countries to stay poor for the sake of the environment when we got rich by fucking the environment?

Here you are assuming a lot about how those countries / populations might analyze the situation. Also, that the path we followed to develop is the only one, and that they are bound to follow our example. That's quite a colonialist point of view.

So the only things that will save the world are globally organized, probably UN coordinated, technological solutions to mitigate the damage done by unchecked capitalist expansion, because we can’t stop capitalism.

If you start from the premise that there is no alternative to capitalism, that this rather young form of social organization is the end of human history, I can understand why you reach that conclusion. But don't assume that your line of reasoning is the only logical conclusion one can reach.