The process of silver mirroring is accelerated by moisture so I am not sure if rinsing or washing the negatives or prints is a good idea, it might aggravate the problem?
The silver mirroring consists of silver sulfide, a very stable compound. AFAIK there is no way to remove it with common photo chemistry, only with mechanical means (abrasion).
Direct toning would make sense, as it would turn any image forming silver in the print into stable silver sulfide, which should prevent it from being oxidized and migrating through the emulsion. So, while not being able to remove the silver mirroring in the affected areas, it could at least in theory stop the print from deteriorating further. However, the question is how this would affect any already oxidized silver (the part of the silver that is already in the process of migration through the emulsion and is no longer part of the image information). If these silver ions are turned into silver sulfide too, this could aggravate the mirroring problem. Not sure if fixing before toning could be of any help to remove exactly that unwanted part of silver in the emulsion.