When you see an object through your eyes, rays emerging radially from the object are focused. The location of the object that you focus to is where these rays appear to diverge from. Your eye doesn't care where the object actually is.
When you wear normal glasses, the glasses themselves are a 'screen'. The main point here is, the rays are appearing to diverge from someplace else. This someplace else is neither the original position, nor right in front of your eyes, rather it is somewhere in between(thats what glasses are meant to do)
So now, all we have to do to make strain-free supergoggles is to orient the screen elements in such a way that they appear to diverge from somewhere. This can be achieved by actually tilting the pixels, or by coating the screen with a thin refractive layer which acts as a lens on short distances..
Now the above solution is partially wrong, as we have TWO eyes, and our ability to judge apprent depth comes from the diverding rays which hit our eyes in slightly shifyed position. Thats how 3d glasses work, they fool your eyes into seeing a shifted pair of images.
With this in hand, the solution becomes simple. Calibrate the screens so that one of them shows a shifted image. We will still have to do a bit of the pixel reorientation as above, but not that much, as you have already fooled your brain on the ficussing distance, now you just need to tweak it so that it actually focuses at that distance.
One more thing to keep in mind is the intensity of light. It must be kept low to avoid strain as well as to make the distance realistic.
EDIT: In this entire discussion, I have assumed the pixel elements to radiate light in one direction (they don't). This will make the "tilt the pixel elements" approach not work. The "thin refractive layer" should still work.