I'd say one thing to consider is where you want the puzzle to lie. If the puzzle is figuring out that you're traversing a 3d object, then it's probably fine to keep it obfuscated initially. If that is just meant to be a common mechanic, then it should be made fairly obvious immediately.
I think one idea would be modifying the transitions between rooms to better "suggest" that you're traversing a 3d object, making it look like the previous room rotates away from the perspective rather than panning off and giving the impression that you're traversing some non-Euclidian flat plain.
I think the hint text in room 6 is a clever idea to get the player to think about the solution, but the button to solve the room is right next to the door you need to leave through, and solving the room gets rid of the text. I'd make it so that the text stays around even after the room is solved so the player can't accidentally delete the hint while just waltzing through.
Another idea would be to create an early puzzle that "forces" a player to circle between 3 rooms? Like having to transport an object between them or something; the solution wouldn't even have to involve the rotation, it just needs to be made obvious to the player in that moment that something weird is going on with the room orientations (this would be a good place for the room 6-style rotating text hint).
Just some ideas. I've never made nor do I plan to make a puzzle game, so take them with a grain of salt.