Good job being creative with this unique puzzler. I liked the use of the screens as the faces of a larger dice - it really tested my spatial reasoning skills (which are bad it seems). I do agree with TobBot2 that adding a 3D element would make it easier for spatial reasoning.
One solution may be having a 3D cube minimap, with the room sprites places on the faces of the cube. This isn't too hard in Unity - I did something similar for my own dice in my game. I built 6 planes with sprite renderers for the 6 sides of the cube. Then add the room sprite to each side of the cube. Then you could automatically move the dice as the player enters rooms or let the player rotate the sprite with mouse drag or keys to plan their moves. The hardest part would be whether it is big enough to be useful.