I want to do academic psychiatry or something like that, as close to a professor in philosophy of mind, and less so seeing patients
I am impressed that you want to have such an open mind on the human mind. However academically, certain majors & professions push people into certain directions for better or worse.
Eric Kandel was for example a psychiatrist by training, but wanted to branch out to do other things such a research in the neurosciences. He went on to do some incredible things. However the currents of medical school push people into residency that then push people into practice.
You of course do not have to follow that current, but will do so at an incredibly large amount of debt.
Another track that may be too late for you to consider if you are already going to medical school is being a psychology Ph.D. since if you were a psychology professor, you'd have the oppurtunity to interact with several other departments in a college or university.
Another factor to consider is that psychiatry is the application of the medical sciences into treating mental illness. We psychiatrists are not trained to understand as much as of the human experience as possible. Our training is limited to the treating mental illness. Psychology is the study of the human mind in general. Mental illness is only one aspect of several things that can happen in a human mind.
you could become an academic psychiatrist, working with psychologists and doctors of other fields if in a university setting.
In any case, you still have plenty of options, and you can still pursue the unorthodox. However be mindful of these currents are there for reasons, and can make things more difficult for you if you decide to paddle against it.