>>1019051 (OP)
Not sure about the docs, but here's my experience:
Only tiling WMs seem to work well with multiple-independent-monitors setup.
I use i3, and I added several shortcuts for 'send workspace to output X'.
As long as you don't ever need to stretch a window over several monitors, this works best.
I still try once in a while to get this behaviour in the KDE/Gnome/LXDE setup, but to no success yet.