For unknown reasons, probably having to do with the unmitigated disaster of trying to get an SDRPlay radio working with GNU Radio (about which, more later), Unicode keyboard input stopped working. This is not to be tolerated, because engineering notation requires a lot of Greek letters.
Unicode support seems to be baked into the lowest levels of the Linux operating system, although it’s not clear to me whether it’s in X, QT, GTK, or somewhere else. Googling the obvious keywords was unavailing; evidently this feature never ever fails or, more likely, very few people use it to any extent.
Note that I already have the Compose key set up, but Compose sequences don’t include Greek letters.
After considerable flailing, I added the Simple Greek keyboard layout and defined the (otherwised unused) Menu key as the keyboard layout switcher. That’s a pretty big hammer for a rather small problem; I devoutly hope Unicode mysteriously starts working again.
For reference, the Greek keyboard layout looks like this:
I’d have put Ω on the W key, rather than V, but that’s just because so many fonts do exactly that.
The Smell of Molten Projects in the Morning 
I know you’re not keen on futzing with Compose settings (for excellent reasons!), but there’s a chance that it’s already baked into your Compose key setup. See if there are any references to ‘dead_greek’ or ‘GREEK SMALL LETTER’ in your /usr/share/X11/locale/en_US.UTF-8/Compose (or wherever it lives). I had lots of references, but xmodmap -pke didn’t match the modifier key. I never use right Ctrl, so I did xmodmap -e ‘keycode 105 = dead_greek NoSymbol Control_R’ and qwerty with right Ctrl becomes χωερτψ
“man XCompose” is a start. So is running xev to see what keycode events different keys produce.
[Ed: Inserted Greek references]
ack: that was supposed to read: See if there are any references to ‘dead_greek’ or ‘GREEK SMALL LETTER’ …
[Ed: Done!]
Technically X (and GTK and the rest of it) are applications, hardly “the lowest level of the operating system.” Still, that’s a frustrating failure mode. My current setup has a key combo that switches languages, that I didn’t know about and kept triggering inadvertently, so I’d be cheerfully typing along and ерут ерштпы цщгдв огые пщ фцкню
Bah! For all I know,
systemdabsorbed it by now.Even if I could figure out where Unicode keyboard processing happens, I’d still have no idea how to heave it upright… but I really want it back, instead of flipping keyboard layouts.