As to the rate, I only have rates of ozone recovery estimated from multi-variate regression fitting, but its very sensitve to what variables are included in the regression.
Of the order of -1-1.5C per century reduction in surface temperatures
seem to come up as a result of accumulation of O3 under ‘stable’ atmospheric conditions.
These are more rate balance equations, rather than ‘accumulation’ but I
use accumulation just to give the general approach.

That is not to say that the current relatively warm temperatures
that I attribute to 5 ultra-plinian eruptions in the last 150 years
are not subject to a more forceful return to a lower temperatures
through solar or some other equilibrating mechanism. In this model, it would
take another ultra-plinian eruption to force the surface temperatures
higher (after a short-term cooling).

Anyway, if you get to the point of quantitative predictions, you know I’ll compare to data.

Right now, it looks like you predict temperature going down, but there is an ozone caveat and you don’t suggest a rate. ( I’m asking to make sure I’m understanding correctly.)

I’d hardly call myself the first to note that volcanic activity affect the GMST. But, clearly, if stratospheric volcanos can affect the GMST, and the veiling remains in the sky for a long time, we expect to see big swings in 8 year trend while they erupt. These are absent when they don’t– and that’s how the data look.