That is my very rough understanding. They do a number on your gut, and they probably significantly alter the balance of the microbiome, but they don't give you a clean slate by any means.

Not sure what the term of art is for the "poop pills", but feels like something like that would be required here. Maybe specially tailored to out-competing the bacteria in question.

Likely there will be bacteriophages in the environment where the Desulfovibrio arise that target it, those could make for a very specific therapy (assuming the causal link holds).