I really don't like super bright monitors and the LED backlight even turned down is a bit much.
Did you turn the brightness down all the way to 0? If you did then it may be a concern, I have a 2412M on my way which is also LED backlit.
I also have not managed to get them to calibrate to a close enough white point for it to not be noticeable. In the images above you can see the white different, and the slight tint.
To me, the photos actually make the 2311H look more washed out, but I do notice the tint that you mentioned in the 2312HM. If this bugs you so much, this means that you are seeing the difference and may have to step up and get the 8/10-bit panels.
The Model M is not for the faint of heart. You either like them or hate them.
Gerbils unite! Fold for UnitedGerbilNation, team 2630.