I almost wonder about apparition binding. If we make it more like the Ambers' ravens than the hounds it might be something we can teach an apprentice. Being able to summon guards on command would be a hell of a thing on the Journey.
On the other hand 'journey' for Eike could just be plopping herself on a couch and doing independent research, it is not like she needs to work for the funds to do that research or seek out books.
... I really don't think appartions would help. Look at what a fresh journeyman can do: Mathilde had a few intro grey spells. The particularly ambitious ones coming to K8Ps had more, but not that much. Magic 3 to 4.
Meanwhile, I'm pretty sure that binding an external quasi-daemonic entity to your soul is a bit more complicated and dangerous. It's battle magic territory, and not the friendly babys frirst battle magic like the teleport of miasma,
and for the Greys it's also
new battle magic territory. I'd say it's Magic 6 or so at minimum. That's stuff you do as a magister.
And guards? Eike already has a super power more suited to summoning guards. It's called money. Hiring a bunch of people is a much safer option for the integrity of her soul.
Personally, I think her journey is going to be something like this: Eike gets put in charge of the EIC (she was probably doing some work there already as a senior apprentice). She works for a few years. At some point she decides she's ready for the exam, and and uses some impressive feat from that work as her mastery (some international negotiation, or breaking a smugglers ring, or something. There's plenty of opportunities). There's plenty of danger, but not danger of personal harm.
If she does some magic research on her private time, it's because she enjoys it (and has a skewed view of normal), not because she has to. Also, because Mathilde has probably using her to battle the backlog, and so she's under the impression that groundbreaking papers are expected.