I am in the same situation as you. The district librarians and I have worked out a tentative plan for book distribution, but it is all subject to change at any moment.
Right now the plan is to review how to use Destiny Discover to 'shelf browse/look for books' and request books. Books requested will be pulled, checked out, and be delivered to the cohort during homeroom or a specified time that works best... our school schedule is still being worked on.
I am working on a book return bin of sorts for each cohort, so students can drop the book in a designated location in the cohort classroom, and then my aide or myself will regularly pick up books, quarantine them, and then check them in. Again, this is a work in progress.
I would love to bring a book cart in for students to look through, but right now the direction in my district is that no student can handle another item a student just touched....which makes looking through a cart of books not an option.
As far as my schedule goes, I am flex, so I will be working with teams to set up a schedule of my lessons, trying to only work with one team per couple of days so I am not crossing teams and grades daily. This idea will also be used when delivering and picking up books.