I have the Hoodman unit that is nominally for a 3" screen, but it covers the 3.2" screen of the D800 without a problem. I hold it up to the back of the camera with the plastic cover in place and can see what I need to see. I don't do video, so I'm not sure if the hand-held approach would work for you, but I think there is a mounting bracket that can be purchased.
I have an old one (MHE52C2) that was made for the 5D2. I had to modify it with a TriPod plate to fit my D7000, but it fits the D800 as is. You can attach a large rubber band to keep it tight or use as is with the hinge that allows you to swing away from LCD when/if needed.
I would contact them to ask if they have anything new that works even better.
I have the Hoodman and as stated earlier it pretty much covers the whole screen, I sometimes have to "look" around to see all info. I use rubber bands to hold it in place. I was an early cheerleader for this product on this forum... but honestly it sits in the camera bag way more than on my camera. I am shooting more and more video and I now would not recommend it. Looking at the CAMAX myself.