The solution is to recognize that this overdue measure is simply part of an accumulating snapshot fact (see The Data Warehouse Toolkit, 2n ed., Ralph Kimball or http://www.kimballgroup.com/2008/11/05/fact-tables/), that tracks the status of a book over time as it moves through its checkout/in process.
There's nothing wrong with having an accumulating snapshot fact like this in a cube. You just have to understand what it is and how to query it. In this case I want to count the occurrences of each value that appears in this fact and the easiest way to do that is with a sql group by rather than mdx.
The answer is he sql in the original question. There is no mdx solution for grouping by a measure value that I am aware of. MDX is the wrong tool for this query.