Libraries are not picky about having the same type of library experience as that is hiring. They look for experience that matches their advertised need. You can easily get those skills in other types of libraries. You must "sell" your experience and skills to match their needs. No one will assume you have the skills needed.
You should write different cover letters for every job you apply. You should also have several different types of resumes ready for different types of positions and/or libraries. You should tweak your library for the job you apply, so that they do not need to guess if you are qualified. Using the words in the job ad is the easiest way to demonstrate the match.
If no one else volunteers, I would be willing to look it over. But, it is a very busy month so it may take a couple weeks.
I recommend you look into the NMRT Resume Review.
Brian C. Gray
Head of Reference & Engineering Librarian
Kelvin Smith Library
Case Western Reserve University
http://blog.case.edu/bcg8bcg8@case.edu
