Enjoyed the game, looking forward to seeing a full version.
I wanted to suggest some kind of short sprint mechanic, maybe you can run faster for a short amount of time but it also makes you louder, widening the distance where you can be detected.
You could also add some kind of mechanic where Mario has some kind of disguise or cover to hide under. He can move with the disguise/cover over him, but he has to freeze when the princess is around or he will be detected. Maybe he's wearing a koopa troopa shell and has to hide in the shell when the princess is around and pop-out again when she passes.