I've gotten into an argument about whether "Most of what I've read is books" or "Most of what I've read are books" is correct. I think it should be "is" because "most of" refers to "what I've read" which is singular but my friend insists it should be "are" because "most of" refers to "books" which is plural.
Maybe you can simply change the construction: Books are what I've most read, or, I've read more books than anything else, or, I've read mostly books. In your example, books ARE what you have read most, so I would agree that in diagrammatic reasoning most of what you've read ARE books. Of all of the various materials I've read, most ARE books. Therefore, because MOST refers to books, and BOOKS is a plural noun, I'm sorry to say that your friend is correct.