Create a specific backup schedule

The built-in backup tools won't get you there unless you are willing to fiddle with the configuration every month.  The built-in tools won't handle a monthly cadence, and there's no ability to rotate the folders (or add a timestamp to the backup destination foldername).  So you'd need to change the destination folder and enable the schedule the week before you want the backup to run, and then disable the schedule afterwards.

If you are willing make the backups weekly, a somewhat different way to get there is to use snapshots on the destination share.  Then you could access previous versions without the problem of managing the folder rotation using the snapshots.

Anyway, if these are hard requirements and the backups need to be fully automated, then you will need to look at other tools (using ssh if you need to put them on the ReadyNAS).  If you are backing up PCs to the NAS, then you could also look at PC backup tools that have the versioning you want.