What a great idea!
Another thing you could do with this is use the dice element to adjust for relative skill levels of the player. For instance, a kid playing an adult could use higher die sizes as a balancing factor.
Yes! This is part of the idea behind the “Dice-Type Swap” variant, though having the extra difficulty of determining which die is which piece for which player might make it more of an obstacle than an aid…
Hmm, perhaps instead, a kid could roll “with advantage” (roll twice and take the higher value)? Something I’ll have to test!