I think maybe a good way to go is a compromise - Since you're already taking efforts to protect privacy without needing to trust you, thats already a good start. But maybe you need some kind of ID to tie behavior together, so you do record one temporarily, until you've processed it into an aggregate (anonymized individual behaviors)

Basically, train a machine learning model on the data of invididuals. You don't want to overfit or that could be de-anonymizable, but a slightly underfit model could capture most of the important patterns, while throwing out most of any identifying aspects.

The hard part then becomes finding a way to demonstrate this actually is happening so that you can be trusted. Unfortunately I can't think of a provable way, since you pretty much either can track users by IDs or not. And if you do..then trust has to be assumed