I see two problems with the solving animation - it is fast, and also you can't tell what the intermediate goals are. To your point about giving visual hints - I've toyed with the idea of highlighting the cubie that is being moved and the position it is being moved to. (One problem with this is when you are trying to re-orient a cubie that is already in its correct position.) Also, perhaps add pauses to delineate sub-goals. I think the best thing to do would be your slider suggestion, perhaps with markers along the slider indicating waypoints toward the solution. And, of course, make the slider bi-directional so that users can go forward and backward. As far as slider - I'm debating whether to use an HTML native slider, or create a cool custom 3D one using THREE.