How to unmount WebDAV volumes using Carbon without long lock period?

I am trying to unmount a WebDAV volume (mounted with FSMountServerVolumeSync ()) using either FSUnmountVolumeSync () or FSEjectVolumeSync (). So far, I have been unable to get any of them to turn off the volume reliably without blocking for more than 20 seconds. While they are blocking, I see that webdavfs_agent is complaining to Console.app that the WebDAV server is not responding. They never fail, however, and the WebDAV volume has always been unmounted. It's like I missed a step.

I think this is wrong, or is it just an OS X bug? The documentation is rather vague as to how much the differences exist between the two methods, or any prerequisites for calling them.