What happens when sulfur enters the stratosphere is quite well known, since we have studied what happens when volcanoes do it.

Unless you think "natural" sulphur from volcanoes behaves different than "artificial" sulphur, maybe because it is blessed by Gaia, of course.

https://earthobservatory.nasa.gov/images/1510/global-effects...

Errrr, we know what happens when you put a roughly Pinatubo plume-sized mixture of Pinatubo plume composition in the vicinity of Pinatubo in 1991.

Everything from there is a generalization and abstraction which is very hard to do with complex systems like meteorological ones.