I like the idea of this repository. Did a quick web search to find it, if I hadn't found it, I would write my own version!
Anyway, I'm building on a bunch of codebases, which are mostly ReST style.
Instead of using docrep, have you considered using docstring-parser? - It supports ReST, Google, and Numpydoc.
Interested in your thoughts @Chilipp; depending on your perspective, happy to work on the PR.