Cool concept, although it kind of feels like the different dice don't really matter. As it stands you don't really know how much health enemies have so I just sort of used whatever dice I had at the moment.
The idea might make more sense if the dice did different things, like a d6 is a projectile or a d20 is a big aoe. Just something to make using the dice an actual decision. Obviously making all 6 dice included unique would be a lot of work for 48 hours but even if there were only 2 or 3 I feel like that would go a long way.