How can I disable the "No Backups for x Days" from Time Machine?
Figured out the completely non-obvious solution. In the Time Machine preferences you have to right-click on the drive icon and then select "Stop Using {Drive Name} for Backup".
Extremely terrible UX, but at least it's doable!
I suggest you get TimeMachineEditor and set your backup schedule to once a week or some time period you find more suitable. This app overrides the hourly backup default schedule of Time Machine and lets you define time periods to prohibit backups.