Hey, thank you!
I think that if there is a fundamental problem here, it might be with the game's incentive structure. One, highrolling on a given floor has a very high expected value that affects the player for the rest of the game -- two, I think the game is not good at communicating the future value of a skill you receive.
One of the games I was inspired by is a little minigame collection named Chinese Parents which has a very similar skill progression system, and their approach was basically to do two things:
- Link each skill to a passive action -- you could choose six passive actions per turn, and each one provided guaranteed growth in a relevant stat.
- Provide intermittent exams which would judge the player on a known list of skills. These exams awarded the equivalent of EXP and the game provided a passive HUD that would warn you in advance about which skills you had failed to develop.
There were many, many presentational problems with this, and the numerical balancing of the game was somewhat flawed -- but I think the fundamental idea was really good, and I think the combination of choices they made caused the game to overall tend towards specialized builds.
I think if I were to develop this further I would probably come up with a system that accomplishes the same thing, but via a more simulationist set of interactions than Chinese Parents used. ("These three thralls _already exist_ in the world -- you won't see more unless you woo them -- as a special deal, you can woo them with a skill that would not usually be effective for that purpose.")