Erik,
I'm a little confused here. The mediation committee has indicated that they would like to be the sole administrators and moderators of the mediation message board. You appear to have taken this request as personal criticism of your good self, and as a result have robustly defended yourself. I think you have certainly made your point of view on the matter clear enough, and I'm sure it is clear to all readers that your actions are without defect. Having established that, let us now move forwards.
It appears that the mediation committee would *still* like to be the sole administrators and moderators of the mediation message board, *despite* your actions being entirely error-free. I think this is an entirely reasonable request. By agreeing to this request, you would be in no way bringing disrepute on yourself, or casting any doubt on the validity of your prior actions as moderator. Indeed, the ability to gracefully hand over the levers of power, where appropriate, is a highly prized ability amongst leaders.
If there are some important reasons, that we are unaware of, why it would be dangerous for you to allow the mediators to administer the mediation message board unaided, I'm sure we would all like to know. Otherwise, I hope you will shortly make all the mediators admins, as they have suggested, and thus free up your valuable time for other things.
Cheers, -Martin