I found the problem. It looks like sometimes quote marks are required for parameters, and sometimes not. For example, the following query string works:
...?key="2b4ad530-fadc-4a4e-bfad-cafad8bda9f8"&include_docs=true&latest=true&descending=true&stale=update_after
Note that the key parameter value requires quotes marks, and the stale parameter does not. Dropping or adding quote marks to make them consistent results in a 400 response. Is this by design?