@aral weird that Gnome doesn't include compose-key as an option without an extra tweak software. In KDE, it's built-in as an option in the keyboard prefs.
Side-note: Glad you like you Gnome desktop, but know that KDE really does the human, end-user design right too. About everything Gnome can do is available in KDE along with a *lot* more.
Don't waste time investigating since you're happy as is. Not trying to get into that KDE vs Gnome argument, just note that they're both excellent these days