What a neat idea!
You’ve made the steps so even, though, and each gap so gradual, it doesn’t seem like there’s much opportunity for the die to get much of the quarter or half turn it would need to start rotating forward.
Much like a real life staircase, I wonder if you couldn’t avoid sliding by flattening out the steps to be a little more horizontal, and start a tumble going by removing a step near the top.
Also, if gravity serves you well, the die will be at its fastest immediately before hitting the “ground” at the bottom of your tower. If you give it a little more space to roll or bounce at the bottom, that might help turn the accumulated momentum into the unpredictable roll you’re looking for. (Couldn’t quite tell if that’s the clearance you were getting at, or if you just meant for ease of picking it up.)