So, after a process of trial-and-error using PowerToys, I've finally found a workaround for my problem.
I set my hotkeys for switching tabs to "Window+\" (since I rarely use \, and it seems this combination doesn't conflict with anything I know). Then, in Keyboard Manager, I remapped it to something like this:
Ctrl+PgUp to Win+Ctrl+\
Ctrl+PgDn to Win+\
It worked like a miracle. There was no need to specify it to work only with Word because I use Groupy and Japanese Typing for other apps too.
For now, I'll stick with this method. Thank you for your suggestion.