Very interesting mechanics!
Now I see why you complained about my AI when I see this clever one you've made, it was fun watching it putting it's plan to work.
I'm guessing it's some sort of backwards targeting? Like it knows what dice it wants to hit and then brute forces its way to see if it is possible from it's current state? Or maybe it's just brute forcing from the current state forward and picking the best result. I would like to know what method you use.
The only thing I had troubles with was clicking on the square behind another dice, but I guess your hotkeys probably helps with that.
Great work!