Well the only way to know for sure is to have an admission by those that are doing it or to actually do chemical composition comparisons of stratosphere air from around the world. So that's gonna be a pretty expensive task. Anyone that would want to do that research would need to be funded on some type of grant, which would most likely be a governmental grant. So fat chance of that happening if they are indeed releasing particulate matter into the air.
And no, I don't think you'd need any more than 10 countries in on the negotiations. US, China, Russia, and India are the biggest polluters by far so if these four were to be reigned in things would get substantially better. But I'd say those four plus Saudi Arabia, Canada, Brazil, Australia, and South Africa would be the most you'd need to plan it all out. And secretive backdoor deals would actually be more beneficial for all of these countries too. That way they can bypass all the politics and nationalism that would stand in the way of progressive negotiations. Not saying I agree with those tactics, but it would be much more efficient than debating all this in the UN.
And of course I'm not saying this is 100% factual or anything, I'm just saying that this conspiracy makes total sense, if you consider the stakes and the political barriers to measures being taken.