Alternative explanations for library usage being down is that paperbacks are already pretty cheap, consumers are interested in a "long tail" of books libraries don't have, and if you want really cheap then you can easily find a long tail of used books for $1-3 on Alibris.
The fact that people are choosing an efficient way to get the books they want is hardly evidence of inelastic demand.
I can borrow e-books from my library, nearly as fast as buying them from Amazon.
I can borrow physical books by hitting their site, putting a hold on it, and then next time I'm in town, I pick it up. It's not UPSd to my door, but it's not that big of an investment. (or, more likely, Wife + kids pick it up next time they bring home 40 books from the library. We sometimes have a good couple feed of the holds shelf.)
You're saying that the middle cost is significant. That suggests that the latter cost is also significant. Therefore lowering the dollar price of the book has little effect on the total in the above equation.
Let's put it another way. When do avid readers start reading a new book? When they finish or get bored of their previous book.
Even if we agree that the total cost (including time) of acquiring and reading a book is high, that does not indicate that demand is inelastic.
Amazon is competing for my leisure time with Apps, Netflix, etc.. It's no wonder that higher priced books are losing out.
The biggest 'cost' to reading a book for many is not the money spent to acquire the book, it's the several hours of leisure time required to read the book, time that could be spent doing something else.
This suggests to me that the overall book demand curve is fairly inelastic.
That Amazon sees more elasticity is not surprising: they're conducting experiments on part of the market. Price has a big influence on what book people buy and where they buy it; but I hypothesize that it has little effect on whether or not they actually buy a book.