I've only got a 12.5 inch but I take the mirror box away from the wiring...and follow the "Krieg" method...I use sterile cotton...
You've got to have a lot of dirt to warrant washing a big mirror anyway...in my opinion. I think you've got to have a lot of dirt on it before it will impact the views.
Like many things, it will never be "clean"...the moment that you finish washing it will begin to accumulate dust almost immediately.
At only a few weeks old I'd be surprised if it needed cleaning already