OLED displays are nice nd all, but the cheapest one I’ve found that is actually on the market is this $4,300 Sony 17-inch, and prices go way up from there, and many that are announced are never actually produced. I would dismiss OLED for any display bigger than a smartphone, at least for the foreseeable future.
PixelQi is unavailable in sizes larger than 10.1 inches.
If backlit LCD isn’t an option then you’re stuck with CRT. The other options are either prototype-only, extremely expensive, or unavailable in sizes for any computer larger than a netbook.
But here is something to try. See, many LCD screens are actually backlit by fluorescent lights which are dimmed by strobing them. They cannot be turned down in a conventional manner, but if you flicker them, you can get the same net effect. It’s the flickering that causes headaches in many, and why I have an issue with fluorescent lighting in general.
Try turning the brightness up. That will reduce flicker.
Some LCD screens are backlit by white LEDs, though I think that is more common in smaller screens (smartphones and tablets).