Accept that, in the case of your append-only log, you need to trust that someone is applying that lack of read permission to themselves. And that they do it well.
Couldn't regular asymmetric encryption take care of that? Just encrypt each entry with the patient's public key.
I think you only need homomorphic encryption if the transformation is something that the owner of data can't or shouldn't do themselves. It would be overkill for simple financial information.
