Do you think this control board is splitting the signal?
I don't think there is any signal splitting in the device you show. That one is just showing two copies of the image on the
same screen, right? So the device will need to
duplicate the pattern in each scan line (repeat it twice in the output line). But it drives only one LCD, with one set of control signals. If you need to use two separate small screens, this device would not work, I think.
But if you can find a single, small wide screen LCD which you could use to display two copies side by side, this could be a solution. But come to think of it: How would this different from the simple VR glass frames which use a mobile phone for display?
An alternative thought: If you don't want a stereoscopic view, have you considered using just a single display and mirrors/prisms to show it to both eyes? Probably a more bulky solution, though.