And they are also the first to cry poor at the slightest hint of donors retreating and grants moving on

Sounds like private schools.

Just run the satirical campaign, satire is an art form and comedians exist XD It's just something fun and different you're doing in between your usual to lighten the mood of all the less fun stuff that all organisations face, surely they understand because they don't act like that so it's not aimed at them right ;D