In matters of health and personal data, not only are there strict laws on the books (e.g. HEPPA), but there remains the matter of trust.
I, too, think in terms of the "freemium" model, but I do so in the context of b-corps, the idea being that stockholders in a b-corp are not free to sue the board over financial matters. What that signals is that the entity was created with no option for exit strategies of the usual kind.
I work on open source biomedical NLP projects which aim to dive into the vast (and messy) PubMed literature, and all of the many databases on health, disease, microbiome, and etc. It seems to me that a project such as yours may end up wandering in similar directions.