Sorry, It's a bit of a TLDR to skim again trough this topic and see all idea that revolved around your Wizard class, but it seems to me what you try to convey with your classes is also a sense of in universe progression for your characters.
I think that could be one of the reason why you ask yourself so much questions. Trying to make character development/personal stories as part of the game mechanic. And also, If I understood correctly, you plan several games, and thus try to plan mechanics in anticipation of the future games, which can only make things more complicated. I for instance plan as well three games, and they will have to have some mechanics in common, but what I'll do is to first focus on my first game, make it works. the other two will only be considered in terms of backstory and foreshadowing. Then if the mechanics of the first one works, I'll expand on them when I will start working on the next installment.
So to come back to your Minuet character, she wants to become Archmage, and so as to study many paths of magic, that makes sense, so are you planning to have all these paths as successive classes? will Archmage also be a class? In my understanding, an Archmage is a title, an achievement, the one who has achieved mastery over magic. It is the end of the journey, not a part of it. so one does not "enter" an Archmage training (that would thus have to be given by another Archmage)
How does the class change happens? is it an inner revelation? is it the manifestation of a formal training?
Also, how is spell craft in your world? Is it mastery of raw magic trough sheer willpower, or carefuland learned application of rote magic and studied rituals?
What I could suggest for Minuet, to make her really stand out, is to do away with Class changes, and instead, have her learn new spells and study different arcane disciplines trough the means of Masters.
This Plugin could help achieve this