I have a PhD in theoretical physics and am coming to the end of my first (one-year) postdoc. However, I have recently discovered that I am far more interested in the philosophy of science than my current work. I read papers in that field and I think I have a lot to contribute, but I don't know how realistic it is to try to publish or apply for academic jobs without a humanities PhD. I probably could afford to do a part-time PhD whilst working in physics but that would be another 6-7 years which doesn't seem realistic. Another option is to apply for a fellowship in the philosophy of science and hope for the best, but I suspect such funding would be extremely competitive. Is it possible to switch careers at postdoc stage? The actual subject of my research wouldn't be so different but there's a huge conceptual shift between science and humanities.

Honestly, I have no idea if it is possible but I completely admire you. Have you considered taking a stepping stone via science communication/outreach? They always struck me as hybrid jobs between science and humanities that you might be qualified for while allowing you to build some good experience for a humanities career.

You already have a Doctorate in PHILOSOPHY, or the study of knowledge. Given your scientific background, I would just go for it. in terms of submitting abstracts to conferences and publishing. If your work is good enough it will get in. Nobody can police your work and request to see your Ph.D certificate to assert you were awarded it in a particular department (in any case it'll say Doctor of Philosophy ;-) .But obviously, your work has to be relevant to make this transition. All the best.