The cloud service does not store backups of files that you delete. However since syncing between the different client apps is not instant, the following may work for you:
Upon completing step (4), you will see the original file be deleted, but the copy will remain and be uploaded to the cloud. The copy will be downloaded from the cloud to your other devices when those devices are next connected to the cloud.
If you delete a folder, you'll want to repeat Step 3 for each file in the folder. I recommend making new folder and copying every file in the old folder to the new folder.