>I don't want FireFox or Chrome reading ~/.ssh or ~/.gnupg or any other directories in my home that it has no business reading.
Both browsers already do this for the processes that are exposed to the internet. The software shown here additionally does it for the entire browser (with the caveat wrt uploading/downloading that I explained, and maybe some more gotchas that aren't immediately obvious).
(You may understand this nuance, but I wanted to point it out, as it's literally what the browser sandboxes do)