The numbers callen suggests sound reasonable.
One thing to keep in mind, though, is that the narrative should try to be in line with published materials. For example, the Greater Alps covenants do not usually extend membership to newly Gauntleted magi, so they have to leave the Tribunal. The Rhine expects lots of service from young magi joining its covenants. Normandy... well, you get the picture.
I'm not trying for the perfect library; but are just saying we don't want higher level summae available?
Re Rhine, I note Peregrinatores are a thing, basically full access to a covenant with a fee of 3 vis/year or one season service in lieu of 3 vis. Not sure if anybody else is from there off the top of my head. But people from the Alps could well end up there too. (And we'll have to host them in our own covenant.)
I am thinking of having some of the years be in the Greater Alps - offering Athena Alpina help as a "special hermetic ambassador" that does what her future role will be: smoothing over relations, easing new policies, gathering info.
She will pay some of her vis source to Athena directly and take small operations for her - sounds ok?
Is your maga and what she can do special enough that someone in the Greater Alps will go against the tradition of "exporting" its newly-Gauntleted magi? Would it not be considered more effective (from the Greater Alps' perspective) to have your maga gain her experience (and make her mistakes) in one of the other Tribunals?
If you think so, make your case to the troupe! 
l was thinking of my magus being taught in Irencillia, given his excessive amount of supernatural Virtues.
Honestly, I don't think this is a path to a mid-high power game, but to relatively low. I'm fine with that, but I think it should be said. Or is it just that we want the pre-game advancement to be limited?
To be honest, l prefer to define games as what they are, rather than as belonging to some arbitrary tiers.
Actually, as we are talking about some 10 years = 40 seasons per character, we could decide on a case-by-case basis.
For instance, if you would go to some pains and try and get into Durenmar, you can expect some nice books there.
I'd honestly rather just cut the post-gauntlet to a minimum. (At least for myself). I don't really enjoy the project of determination by committee.
For instance, if I was writing on my own I would say that Wolfgang ends up as Peregrinatore at Durenmar, in a lab in a lower level of Phillipus' tower. But if I have to convince people of that, or in fact of anything, I'd rather just let it go.
l would suggest you try some year of it first and then decide whether or not it's to your liking.
I like the narrative approach, as long as (as I have mentioned) the overall amount of exp (bar virtues) is approximately the same year for year, across the magi.
I think it's about not cherry-picking. Otherwise you end up everyone's covenant library being absolutely perfect for that individual mage, regardless of who else is in the covenant. On top of this, there are two big perks here, still remaining. First is that you pretty much always get more experience this way than with the core book's 30-10/season method. Second, if you want something better, you can still get it by trading for it; for example, maybe you pay 3 pawns to pick up a Quality-11 tractatus that you now own.
That could be a reasonable solution, actually just buying books hadn't occurred to me.
How are we going to figure out earning vis?
That's a good question.
There is one nice thing with House Verditius for me: fixed prices. However, there are two things that Hannah is likely to be hired to do soon with her potentially high Philosophiae score: open big devices and make Items of Quality. And those two things get wonky with the formula. For Items of Quality the formula says 2 pawns for wages, but you can get that yourself with a Lab Total of 11 and do better with a Lab Total of 21. Meanwhile, someone who can only manage a +3 for a suit of armor isn't likely to earn as much as someone who can manage a +7. Use the vis extraction formula instead makes much more sense here. For opening really big devices, things go the other way, as there is no way someone would reasonably pay 100 pawns of wages for someone to open an item with 50 pawns.
I'm thinking more about giant-hunting/hedge mage hunting expeditions to scandinavia.
Yes, that's why I thought this was a good question. There aren't many cases where it's very clear-cut, or even where there is a good guide.
Such things has to be determined on a case-by-case basis, sadly.
I could propose advancement guidelines if people feel the need for it. How much xp per year, impact of lab work, obtaining raw vis, etc.
I think the narrative approach may well work better, and we can double-check to see that things are happening reasonably.
I meant guidelines on how much benefits (xp, vis, etc.) the various activities described in the narrative approach should yield.
That would be awesome.