How to disable "iCloud Storage is Full" Messages on OS X
As far as I'm aware, these are the only ways to turn off this message:


Turn off iCloud Backup
Free up some space in iCloud
Turn on Do Not Disturb
Pay the money to upgrade


All the Google searches and discussions on Reddit, Apple and other websites indicate that there is no other way. However I'm trying to reproduce the issue to see if it can be solved via the command line.

Until then, or until someone else comes up with a working procedure, assume the above is the only answer.