Narrow runway- glad someone noticed, and liked my idea - even if I was joking a bit.
Of course if you're sick for more then 21 days in a row then you should notify your CAA. However, you're not sick for 21 days in a row, just those 5 days out of every 9 (if you're on a 5/4 roster) for 3 months that you are required to work your notice. They like a doctors note for 3 days or more, but you don't have to do it. Not only are you leaving, you no longer worry about an 'unauthorised absence' on your file!
Just a thought, but maybe worth doing it in the final month of the notice period, as they would probably not pay you anyway (for reasons mentioned above), so once paid on the 2nd month call sick the whole of the last month ahaha