I would remove the metal mesh, no matter what you do burying drywall under it and attempting to smooth it all out with spackle will never work. Then you will be aggravated at having to remove the metal mesh and installing new drywall.

I would remove all the plaster walls and ceiling in the room, and start all over, with all new sheetrock. Trying to butt up to old plaster will show on your finished wall. Its best to do it right the first time, than having to look at all the mistakes forever.

@cat_ky, definitely a best approch but not possible given the time to complete.

drywall comes in 1/4", 3/8", 1/2" and 5/8" thickness, though 1/4" is usually a special order. I would trim all the metal mesh all the way to the corner of the wall, and remove that 12" or so piece of plaster and mesh all the way to where you have a clean line of solid plaster, and measure the thickness between the stud and the surface of the plaster. Use drywall of the same thickness, or combine two or more layers of drywall to achieve the same thickness as the old plaster. Mud and tape as you would any regular drywall seam. Nobody will be able to tell the difference once primed and painted.