What makes a stat increase?
Internalized Lessons: Has a false sense of scarcity, and difficult to keep interesting.
Internalized Lessons only after major events: Makes it an automatic pick which I want to avoid.
Being able to train whenever: Makes it too grindable and disconnected from the events going on.
Other possibilities:
Learn By Doing: It would have to be limited by something. Dice rolls? Maybe just a flat one in ten or something every time a trait is used, for an average of +1 to one characteristic every year? Maybe on a double for the first dice roll per action? This actually might not be a bad way to go about it, but it does mean that the players have zero control over it and can't 'focus' on it.
Skills: "Why did Mathilde learn about this odd esoteric and probably useless thing?" "For the characteristic increase." I'm not sure whether this would be gamey and unrealistic or actually kinda flavorful, Mathilde seeking out new facets of a particular skill to learn. Limits itself because you have to find new things to learn, new people to learn from.
I like the skill option. I guess I'm not too worried about Mathilde chasing useless skills when there are so many useful things to learn already. I mean, right now, we could revise her character sheet so that her magical abilities are tied into skills which are tied into traits and have her be basically the same in capabilities while writing out her prowess in skill/stat form, for something like this:
Petty Magic (Proficient): +1 Learning, +1 Magic
Lesser Magic (Proficient): +1 Learning, +1 Magic
Lore of Shadow (Proficient): +1 Learning, +1 Magic
Expert Lore of Shadow (Beginner)
Matrix Caster (Proficient): +2 Learning
Enchanter (Proficient): +2 Learning
Likewise for other stats- if there's no "internalization" action we can push Mathilde more easily to develop skills that we want to see her use. There are useful skills in
every stat that we don't have. Here's some examples.
Diplomacy - Law, Imperial Noble Culture, Dwarf Culture
Stewardship - Economics, Construction, Fief Management
Martial - Tactics, Command, any weapon skill
Intrigue - Stealth, Manipulation, Poisoning
Piety - Faith of Ranald, Imperial Religious Lore
Learning - basically all our magic advancements, any scholarly topic
I would much rather have voted for Mathilde to study Expert Lore of Shadow, Expert Enchanting, and Faith of Ranald this turn than Learning, New Spells, and Piety. The less specific options are more abstract and general but they're also more
bland.
Combine this with some elements of Learn By Doing- crits could sometimes provide one-level increases in skills (Beginner to Intermediate, etc.) and an action-packed series of events could sometimes trigger trait votes as we had post-Drakenhof, with the traits affecting stats.