So instead of moving the directories I could copy them and then delete each file one at a time. Any file that can't be deleted I could use CreateFile to mark it to be deleted when closed.

Your link led me to GetSecurityInfo which can be used to get security information about a directory. If a delete directory failed I could get information about who has it open. It doesn't look like CreateFile will let me mark a directory for deletion. But I think I'm getting in a little over my head now.

From Creating and Deleting Directories:

To delete an existing directory, use the RemoveDirectory or RemoveDirectoryTransacted function. Before removing a directory, you must ensure that the directory is empty and that you have the delete access privilege for the directory. To do the latter, call the GetSecurityInfo function.