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As rendering goes on, scene starts to fill with black dots, Preview screen becomes illegible with black dots.

check all tons of other posts about problems with SSS from old materials

There are some rules about dilectric and sss materials.

For example I think it was placing a SSS material in a dilectric is NOT a good idea.
I have had black dots trying this and magically solved it by redoing the materials in the end.

I'd follow choochees post and search the forum