I put the "Vello Glass LCD Screen Protector for Nikon D4, D600 & D800" (available from B & H) on my D600. I was able to put in on the rear LCD monitor with no problems; the black border did not cover-up any of the screen. However, the small LCD protector it came with did not quite fit the top LCD screen on the D600; it was just a tiny bit too large to make it stick on the LCD.
This LCD protector allowed me to easily put on the Really Right Stuff L-plate without any problem.
I've only recently put this on the D600 so I don't know about how it will work in the long term.