Hi Benjamin and thanks for trying out Tinkerer!
pages/* is not a restriction, it's just what Tinkerer supports for pages. You can manually alter the master.rst file and add documents in any subdirectory. You won't be able to use the tinker --post or tinker --page command line, you will have to manually open master.rst and hook your pages there, but once that is done, they should be picked up by the Sphinx build.
For the index.html, you can probably tweak the aggregated.html template to display something else. Create an aggregated.html under your __templates directory and tweak it to your liking.
Thank you,
Vlad