I'll just point out that Handbook 2: 12.6.1 refers to "the" ward librarian. So it would seem that LCR is enforcing a strict reading of the Handbook.
The scheduling of librarian/assistant librarians is to follow the goal you've outlined. So there doesn't appear to be a need to change LCR. The only difference from the way you're doing things now is just one person is designated as being the "in charge" person. That might be an improvement, because when you have multiple people with exactly the same responsibility, then no one is really responsible.
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