Since dithering is one of the reasons for led strain, I thought making desktop color-schemes 6-bit might help on 6-bit +FRC panels. I have a positive experience with this approach on KDE color schemes. Please see if this is of help to you too.
Take any of color scheme files from either /usr/share/color-schemes/ or ~/.kde4/share/apps/color-schemes and the save the following python script into a file named transform-color-scheme.py run as:
python transform-color-scheme.py < file.colors > file-6bit.colors
python transform-color-scheme.py < /usr/share/color-schemes/Breath.colors > ~/Breath-6-bit.colors
And then, import this new color scheme and use it, using "System Settings" -> "Colors"
I am neither an expert in designing color schemes nor an expert in dithering (LUTs etc.). So, please ignore any conceptual mistakes. Also, no offence intended to the color scheme authors.