IOS – How to force the iOS device to create a new backup on iCloud

I have an iPod5. I have been using iCloud for backups. However, I have an issue in a particular app that only goes away when I fully reset the device. (The issue in the app persists if I restore from iCloud backup, but that’s not what I want addressed here). So, at the moment, my iOS device is running as if it were a fresh new iOS install. I want to be able to keep going with this install and have it backed up to iCloud. However, I also want to keep my old backup around so that I can go back to that later.

I thought that iCloud would automatically start a new backup series when I chose to set up my iPod5 as a “New” device. However, when I look at the backups UI, I get the impression that I am going to lose my old backup as soon as it performs the next backup.

Under iCloud → Backup, I see “Last Backup: 1:37 AM”. That is the timestamp of the backup I performed on this iPod before resetting it:

Under “Manage Storage” when viewing iCloud settings through the device, it lists the iPod I’m using as matching the backup I made before I set up my iPod as a new iPod. The backup that it says is associated with this iPod is the very one I want to preserve when I make a backup of my iPod:

And when visiting that screen, you can see the discrepancy between the backup that looks like it will be overwritten and the backup that iOS plans on overwriting it with:

So, how do I get iOS iCloud backups to start a new backup or save/checkpoint/rename the old one? I’m starting to fear that my only option is to restore the old backup, make a backup in iTunes, and then manage storage of that backup manually which is a pain that I hoped iCloud would be able to prevent…

In an answer to another question, I read:

• You can have multiple backups in iCloud for a device and choose which backup to restore from (assuming there are no device/iOS compatibility issues).

My question is: how? 😉