Why can't a third party app use each user's individual API queries for that user's app usage? Like you have the user OAuth with the app, and then the app uses that user's own user API access to query the API. 100 queries a minutes seems like it should be enough for most people.
To stay inside the free tier, you get 1000 requests spread over 10 minutes (their current spike-smoothing behaviour) across your entire user base.