I do think a mediator could accomplish these goals. While the conflicts of interest might not be reduced to zero, it's likely that the pool of mediators will have more degrees of separation from the managers and therefore will reduce conflicts. (Whereas the normal employees that are on the jury have to consider the very real implications of their actions if they contradict what an important manager says.)
Meaningful investigations/mediations or tribunals tend to produce surprises, and tend to generate precedent.
There’s no way a company would subject itself to that scrutiny.
I think the mediators would actually have to show that they saved the jobs of some valuable employees from getting fired to get continued business.
If they have a 90+% company win rate then the experiment probably isn't productive.