I've been using this backup/synchronizing software for >10years, and it has "move files to trash if possible" option that works with synchronization mode. kish Designs :: CopyTo Synchronizer :: Synchronize and back up your files
The question is, whether the software can move files on NAS drive to trash (which is a property of local drive) or not.
This software went completely freeware, and the writer seems like stop developing. I used to asked him for additional features, and he was very good at incorporating user requests.