A method includes (a) while processing data storage requests from users directed to filesystems of a plurality of filesystems served from a data storage system, receiving a request to execute a filesystem reorganization task on a filesystem of the plurality of filesystems, (b) in response to receiving the request, checking whether the filesystem reorganization task has both a global reorganization token and a filesystem-specific reorganization token, the filesystem-specific reorganization token being specific to the filesystem on which the filesystem reorganization task has been requested to execute, and (c) in response to determining that the filesystem reorganization task does have both the global reorganization token and the filesystem-specific reorganization token, executing the filesystem reorganization task to move a data block from one location within the filesystem to another location within the filesystem. Other embodiments are directed to corresponding apparatuses, computer program products, and systems for performing similar methods.