I think it would be more logical to provide support for good bacteria. If you had a field with a weed problem, spraying kill-everything herbicide would get rid of the weeds, but also everything else, leaving bare soil for opportunistic weeds. Planting a cover crop that crowds out weeds might be more effective at getting the field back into healthy function.I am happy to share what natural antibiotics you can try. This would be the most logical solution to me.
If you knew which specific strain was a problem, and had an antibiotic that targeted only that strain, then that would be a better choice.
The gut and microbiome have a complex interaction. It seems that the gut cells and immune cells differentiate between good and bad strains, and help the good ones, even helping them form biofilms for the benefit of the gut. As with antibiotics, a kill-everything biofilm buster isn't the best solution for that.
One tactic I don't recall reading about is abrupt changes in diet. The microbiome is supposed to respond fairly quickly to what's passing through, with some strains quickly growing, and others dying back. So, going meat-only for a few days, then high-pectin fruit-only, then whole grains, and so forth, might change the battlefields for the various strains, giving the good ones a chance to win some battles. If you know what the bad strain is, and what conditions it prefers, then you could tailor your diet to avoid what it likes.
Rather than simple tactics (ie. antibiotics), more varied tactics would likely be more effective. The more information you have about the enemy, the better your battle plans.
No nukes. Nukes are bad.