Wall Fix Installing Mirror, Laminating Drywall?

I'm installing a mirror over a bathroom vanity in an alcove. I made a sloppy mistake finishing the drywall below the base cabinets, and there is a 5/8ths inch gap at most between the backsplash and the back wall. I'm installing a 48 inch by 40 inch mirror that will rest on the vanity backsplash. So I think the easiest fix right now is to build the wall out behind the mirror to fill the gap(rather than take the vanity and base cabinets apart). The wall is primed. 1) Should I laminate an extra piece of 5/8ths inch drywall just slightly smaller than the mirror to fill the gap. If so how should I do this? Will the primer interfere with the laminating adhesive? 2) The exposed(behind the mirror) cut edges of the drywall will need to be sealed. Can I just prime these edges? 3) Is there another material you would suggest instead of drywall? I assume that if it is primed over there should be no problems with moisture. Sometimes when people shower without the fan there are little rivulets of water that run down the wall that may rest of top of the new piece of drywall. But the vanity alcove is separated from the shower area. Thanks.

 

How did you get a 5/8" gap between the wall and the cabinet?

Joint compound will adhere to paint although paint with a sheen should be scuff sanded first. IMO a better fix would be to mount a frame around the mirror to hide the difference.