I've seen estimates of the cost of sulfide injection to be about 2-3B / yr / 1C.

That's not outside of the capability of a country like India, much less China

I saw those too. They look wildly optimistic, on top of being based on a wildly optimistic efficiency of the aerosols themselves, compounding the issue. But even assuming that - I read that multiple tens of megatons of aerosols need to be dispersed each year, on a regular basis. That alone doesn't look like a 2-3 measly billion job. Just a small fleet of 10 old narrowbody jets would cost at least 1 billion per year to operate. And someone need to prepare all that reagents, ship them, construct machinery etc. Then there is a problem that GH gas emissions are constantly rising and old gasses are not removed, so the heating accelerates. What requires 10-20Mt of aerosols today, will require more in a decade, then even even more and more. And as soon as injection stop, we are back to square 1 and heating will resume even harder.

Now that I think about - this is actually a motivation for China to do all that expenses. Establish themselves as a monopoly caretaker of the program, wait out until alternative programs will ramp down due to lowering interest, and then start blackmailing the world to conform to their demands or else they will stop injecting sulfur. That would be an incredible power play :) .