I wonder if there's room to expand this further? At the moment, runs end too quickly for the idea of having a build to take root, and the fights are hard enough that you're better off resting, as two to three fights in a row will likely end your run no matter how lucky your rolls are.
Terry Cavanagh's Dicey Dungeons has some good ideas on that front, and not just because it's also about dice! He separates the dungeon into 5 or 6 floors, divides the enemies into difficulty buckets and randomly populates each floor with 2-3 enemies of a particular difficulty one of which is often optional if you don't mind missing out on a shop/item chest/healing item, and the floors get harder as you go. There's also a light levelling mechanic that grants a full heal on levelling up. These things combine to give a real sense of pushing your luck, and the difficulty curve / run length means you get to feel like you're working towards a particular build, depending on what fortune throws your way.
In terms of the fights themselves, I wonder if the weak core would be better off as something more strategic (perhaps even changing between enemies, to give more enemy variety) that can be activated by something less improbable, like a full house. You can still hold out the prospect of a big reward for a yahtzee, but maybe not link it to a core? It could also be strategically interesting to have a core that operates as a longer-term dice-sink, so you're choosing between putting short-term damage into the heart core, or building a long straight (or whatever) over multiple turns in the dice-sink core in order to, for example, increase your attack/block stat (which is a little under-utilised for your character) or heal or something more interesting.