The SO₂ cleans up itself in ~2 years.

I'm not sure what you mean by "cleans up itself" as it doesn't just disappear. What is likely is that it gets distributed through various ecosystems and thus is no longer in the stratosphere. What concerns me is our lack of knowledge about that process and secondary effects on ecosystems.

Humanity has a track record of making assumptions about complex systems and treating them like a simple engine.