Very nice Idea.
I am currently working on something similar, not for the D&D game, but for Earthdawn instead.
Also I don't have the dot-matrix you have but bought a 20x4 LCD Module which I would use for output.
I implemented a mechanism called "exploding dice": If you roll the highest number possible on a die, you can reroll - as long as you roll again the highest number.
Additionally there are different Steps for the Skills witch translates in different dice-sets to roll. It begins with
Step 1: D4-2
to
Step 10: D10 + D6
and so on...