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.

Because it’s too late for those options to work.

And the solution is what? To pollute the climate with sulfur dioxide, initiating another mass extinction and the social murder of millions of people through disease and starvation?

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

And your solution is what? Find salvation in technology? There are no technological solutions to social problems. You can't engineer your way out of ecological crises. Ecological crises are intimately social crisis, so the solution to ecological problems are found by addressing social issues. Technologies are deeply embedded in a social matrix—technologies are things that exist in specific social contexts. Your very justification is based on the premise that greenhouse gas emissions cannot be cut, thereby justifying a technological solution that allows the continuing dumping of greenhouse gas emissions to the atmosphere. See how this technology serves to only entrench climate injustice?

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?

There we see your bias, that you cannot imagine a fundamentally different way of life that what bourgeois ideology tells you about. The solution to the climate crisis doesn't mean poverty for all—though a failure to solve the climate crisis will mean poverty for all—but rather that well-being and standards of living ought be disentangled with emissions. Solarpunk technologies and philosophies already give us insight into what kind of technologies can be used to disentangle the good life from bourgeois standards of living and the carbon emissions associated with it. Instead, you essentially assume that solarpunk is impossible (or rather that genocidal projects like geoengineering is solarpunk), thereby already dismissing the plurality of what life could be in a post-carbon world.

I support geoengineering because, frankly, it’s the only hope left.

Then the world you support is dystopia, climate chaos, and genocide, because to be clear: geoengineering will kill millions in ecological devastation, drought, and geoengineering-related diseases. Those on the side of climate justice will oppose geoengineering just as much as we oppose the system that is destroying the world. When the time comes, we will see which side of the barricades you find yourself.

Does taxed carbon do less damage to the environment? My guess would be that the only thing that would happen are increased consumer prices. Wealthy people simply pay their "pollution fee" and keep going.