Thank you very much for a thorough feedback to our game.
The looks of the tutorial is currently a high priority item on my TODO list, but I intended to rework it completely and change it into some kind of dialogue (similar to the ones you see after defeating each monster for the first time) so it will take me some time to do that.
As for the overflowing numbers, do you mean in the combat stats UI? The rework on these parts is scheduled as well, I practically did not touch this since the GMTK jam ended, so it sure need some polish. I also intend to rework the combat animations so it is more readable what is going on, including all those flashy red negative numbers indicating damage and so on. If only there was more time!
You are right, that the strategy is mostly "put the big numbers in the squares". It gets a bit nuanced later on because you might want to save leveled up dice for another round if your roll was a bit unlucky but I agree that some element that would let you strategize a bit more would improve the gameplay significantly. It got a bit better when I introduced the monster abilities (these were not there for the GMTK submission), but it's still pretty much in the "use big numbers, don't use small numbers" state. I am thinking of adding elemental dice that would work better when paired with the right action but I also don't want the planning phase to become some tedious overoptimization until the best solution is found.
The diceholder has not been tested all that much since I added his mind control ability, so there is a real possibility he is currently too OP and would deserve a nerf. As for distinct hero roles, this was one of the more difficult parts of game design, because when we initially had the hero actions very distinct and characteristic, the game was not playable because you'd often roll useless actions (too much defense and heal and not enough attack). By adding more attacks though, the heroes lost a bit of their distinctiveness. I am not really sure how to solve this properly, maybe we could have more than 1 or 2 symbols per hero face (like 2-4 on each hero every turn)?