I really like this solution you landed on. I very much enjoyed the level of difficulty of the ONYX Linking in Sephonie, so having a similar difficulty for this sounds great to me. The gentle music/sfx in the video is nice too!
You mention there's a bit of luck involved. If I understand correctly, that comes from the fact that the room you get is never 100% guaranteed — so you could do everything "correctly" but still get a bad room. Would you just have to reset the world at that point? Do you think resetting/retrying like this would be tedious when you know the "solution" and just have to get good RNG?
FWIW, the board game Black Sonata came to mind when you mentioned "puzzle games where you 'deduce and then test the answers'". This video does a pretty good job of efficiently getting the idea across (the guy in the video is kinda goofy sometimes though lol). The "test the answers" part happens about halfway through the video FYI. It's a deduction game with an interesting physical design. Some cards have holes in them that you lay over other cards. If you see a symbol through that hole, that means you've correctly deduced something. I also see some similarities to the "shuffled world" in how the Dark Lady moves around.
Anyways, this post was really interesting to read! It's helpful (and entertaining) seeing how you work through issues. I'll probably try this "write a blog post" method next time I'm mega stuck haha.