Thanks. I had checked that page multiple times, but now, after several attempts, I’ve managed to figure out XModMap, allowing me to set an arbitrary key as the “muhenkan” key, which switches between hiragana, katakana, and also half-width katakana (which I didn’t want but it’s still a better setup than what I have on Windows).
After downloading xorg-xmodmap and xorg-xev, I used xev in Konsole to figure out the keycode for the Pause key (127), using the line provided in the ‘Identifying keycodes in Xorg’ section of the Arch Linux ‘Keyboard input’ page:
xev | awk -F'[ )]+' '/^KeyPress/ { a[NR+2] } NR in a { printf "%-3s %s\n", $5, $8 }'
From there, all I needed to do was open ~/.Xmodmap (which is auto-loaded by the Xmodmap process in ~/.xinitrc) and add this line:
keycode 127 = Muhenkan
then, back in Konsole, reload the bindings with XModMap so I wouldn’t have to restart the computer:
xmodmap ~/.Xmodmap
and everything seems to work now. I press Ctrl + Space to switch to Mozc, for which I’ve set hiragana as the default input, and I hit the Pause key to cycle through katakana and half-width katakana.
Apparently, if the keyboard is unplugged momentarily, the custom key mappings are lost and the user will need to reload them with the command above. But I don’t anticipate that to happen much at all.
So thank you for the advice, I guess it just took some time for me to better learn the tools I needed.