Charging for the API wouldn't be a problem if it was either cheap and short term notice, or expensive and long term notice. The biggest problem is that it is both extremely short term notice (a month) and expensive as hell. You don't do this in good faith if the goal is to provide a sustainable business; you do it if you want to kill the API, but have a fallback "despite our best efforts" angle to work in PR pieces.

Providing a per app, per user API key would be the most sustainable way of doing business with 3rd party app developers while keeping users that are willing to pay happy. Plenty of the users that use 3rd party apps already pay something to use them, so it's not out of the question that they would be willing to pay even more to keep using them. I know I would.