I have conflicting thoughts about this. I'm thinking that the military and Library aspects, respectively, don't mesh well. I know they are two contrasting concepts — and that's fine! They're each going to grant the reader a different feeling. And you can make that work, for sure. But I don't think each of these two aspects is as strong as they could be on their own.
For instance, the military aspect does not evoke "orderliness" and "hardiness", which are the first things to come to mind when I think "military". It instead feels unprofessional, like running blind into conflict with no attempt at making communications. And the Library aspect, while containing some "magic" (like the music coming from a strange place, a book emitting "eldritch light", and shelving rows housing just about every topic you can imagine, esoteric or otherwise) is also devoid of life. This may be a difference in headcanon, but it didn't feel, to me, like the Wanderers' Library — but instead, like any old, mundane library.