Alright, I've got some ideas.
Generate dungeons by picking "cards"; a series of encounters followed by the loot. These encounters would look something like "test higher of str and dex" with certain consequences for success or failure. Get through a certain number of cards and you get the reward, easy.
Rather than just stating a single word as their character's Attitude, they have to set a few different parameters, like programming an AI. Some encounters will probably have "Opportunities" which the character then rolls their attitude to decide if they take or not. For example, if a character in a party stumbles into a teleport trap and gets kidnapped by the dungeon, the other characters in the party check their "help friend" attitude to see if they're willing to take some extra encounters to rescue that character.
Between delves, you get a list of dungeons you can visit. If you're visiting the same dungeon as someone else, you can group up with them to cooperate and split the loot. If you don't, you're instead racing to see who gets it first.
And my impression of what the stats should be:
Vitality: Max HP. If you run out of HP, you die. Tested rarely.
Attunement: Max MP. You can usually "use magic" on tests, which costs 1 MP and lets you add Mind or Heart to that test. Tested rarely.
Valor: Strength/Bravery/Aggression. Tested often.
Discretion: Agility/Perception/Stealth. Tested often.
Mind: Intelligence/Will. Used for magic. Tested rarely.
Heart: Empathy/Charisma. Used for magic. Tested rarely.
Luck: Some tests use luck. But it's not something you can train! You always have 3 luck unless you're cursed/blessed or something.
As for classes, they provide special abilities which trigger in some circumstance. Like healing when a party member has low HP, raising a skeleton after beating monsters, etc.
Feels like this is getting away from me a little, but I think it should work? Guess I'll have to test it some time. >.<