So what about adding the feature to mute a mod/site owner, but allowing them to reserve the right to override it in the case of important circumstances such as site wide announcements etc.

I accept that this would be open to abuse but it would also solve such problems and establish a code of conduct where in abuse of the system would be obvious (e.g. a muted member overriding it for a reason not covered in the newly established code of conduct).

Of course there is development time required for this - but as a concept what do we think?

The alternative of course is to simply ignore people I suppose