jordan
Today, my ASRock Arc A770 arrived. It seems that HDMI on it is routed through DP. Check your A770 LE in Ubuntu Desktop (X11); if it's the same for you, you won't have any issues setting 6 bits with the xrandr utility when connected via HDMI.
They mention here that LE also doesn't have a 'true' HDMI (https://www.vegascreativesoftware.info/us/forum/intel-arc-general-discussion-of-newest-gpu-competitor--140323/), and most likely, inside the graphics card, it is connected via a converter to DP.
You can check with the command
xrandr --verbose
You should see something like "DP-X connected primary…". If you see something like that, you can set it to 6 bits with the command
xrandr --output DP-X --set "max bpc" 6
where X is the number of the DP output.
My HDMI connection is detected as DP-1, which indicates that the HDMI port in it is not genuine:
DP-1 connected primary 1920x1080+0+0 (0x4b) normal (normal left inverted right x axis y axis) 531mm x 298mm
Clones: HDMI-1
max bpc: 6
range: (6, 12)
subconnector: HDMI
P.S. Regarding dithering, I can't say for certain yet. It seems that after switching to 6 bits, everything is okay, but more time is needed for testing.