I understand you want really hard to believe in what you're saying. But you should believe them when they say "no third party applications using OAuth".
It's irrelevant if you're paying them. They say clearly 1P apps are ok; 3P apps are not. Yours is 3P, so you're breaking the ToS.
Will they care? Probably not. At least not until you become popular enough to show up in their dashboards. So you should be fine for a whole, until you cross some threshold and they decide it's time to close the loophole.
It's irrelevant if you're paying them. They say clearly 1P apps are ok; 3P apps are not. Yours is 3P, so you're breaking the ToS.
Will they care? Probably not. At least not until you become popular enough to show up in their dashboards. So you should be fine for a whole, until you cross some threshold and they decide it's time to close the loophole.