> How are you supposed to deal with recalcitrant users?

Keep the servers running, but make the recalcitrant users pay for the costs and a then some more. It is actually a common strategy. Big, slow companies often have trouble with deprecation, but they also have deep pockets, and they will gladly pay a premium so that they can keep the API stable at least for some time.

If you ask for money, you will probably get more reactions too.