Here's a simple suggestion. Carve out a portion of the Prime fee for book borrowing, say $12/year. Since you can rent 1/book per month, each publisher gets $1/month per borrow. Someone takes six months to read your book, you get $6. 1000 people check out your book this month, you get $1000.

The price is just an example, but it seems a reasonable compromise. Fixed fee for the customers, variable fees for the authors.