I cheat :) On GNU/Linux (well, X11) I use keynav, a nice little utility that lets you drive the cursor by keyboard. It's often a little clunkier than actual mouse, but you don't have to take your hands off the keyboard and it covers the "I only need to click that one button that somehow isn't possible to hit from the keyboard."
Strange. I don't think I have a compositor running (i3 wm, not much graphical fluff). Would you mind trying https://github.com/yjftsjthsd-g/keynav and if that doesn't work open an issue? (That's "my" fork, albeit with basically no code from me; I discovered that a number of folks were running separate forks and built a version merging as many as I reasonably could. I think one of them changes the way it renders onscreen and so may have better luck.)
