Eww, sounds a bit rough. Unbindable controls in this day and age? Gotta wonder why they're not using some open source input mapping library that supports both dInput and Xinput.
Do we know if the writer is someone other than one of the main staff? Cause if the writing level is Rick & Morty or BBT levels of eyerolling self-referential humor, that could be a bad sign towards how open they are to feedback.
Ask politely and X Plus is likely to listen (over at Steam ...). Whether they listen and
care (over at Steam!)? When it's reporting bugs and pointing out improvements, sharing your experience, they will. Unlikely they change story as it is so close to release. ;-)
Being a Unity game ... they will fix the input system. They even hinted on a patch for the demo, which, like Syberia's, will likely never finds its way to GOG.
Add: As regards humor, self-referential or otherwise, maybe it doesn't translate all that well from Japanese to English and other languages. It is a game made by Japanese developers after all. Doesn't mean the English script can't be changed to adapt to western sense of humor. It's all text output so ... if they wanted to, translators could. ;)
Add: Inspiration, I do have the strong feeling that one of their inspirational sources for the challenge stages must have been レッドアリーマー 魔界村外伝 or Gargoyle's Quest as it is known here.