I do believe people are over-thinking this problem a little too much. Has anyone stopped to ask the very simple question, "how DO you solve a Rubik's cube?" There is some intelligence and pattern recognition involved in terms of knowing the center squares are stationary and recognizing how the rest of them turn, but the ultimate key to solving a Rubik's cube is just putting in the time to experiment and learn all the patterns in the first place.
So, the incredibly beat-your-head-against-the-wall simple solution is to just say the Ravenclaw lady was too busy with other things to put in the effort, and was unaware of anything that would have made the task important enough for her to spend that much time on it. (And maybe give it a simple immunity to magic to prevent that reverse-twisting method. Or, for an even more mundane solution, have the coloring of the squared intelligently assigned to the squares pre-scrambled such that it is solvable, but the reverse-twist spell will not solve it.)
With this solution, the reason the protagonist is able to solve it is not because he is "modern," (the vast majority of modern people can't solve a Rubik's cube either,) it's because he literally has nothing better to do. (Trust me, if it's something the audience can identify as nothing special, it is a LOT better for the story to deprecate your protagonist than it is to glorify them for doing something like this.) Of course, to sell that one you'll need to make him solving the cube a long-standing thing that he keeps at for several chapters going in the background. That, or show him solving Rubik's cubes in his non-wizarding life before encountering this one, thus showing he's already developed the skills for solving them somewhat quickly.
At that point, the only thing you need to somehow explain is why she hadn't just handed the task off to some grunt working under her, but that can be pretty easily explained as her figuring that they'd be no more capable of solving it than her. A bad assumption to be sure, but that could be the point of disconnect she'd have that a modern person wouldn't.