Given the example of being able to write stuff to the ssh authorized_keys it would be prudent to simply chroot your redis installation. It seems like a easy, if somewhat old fashion solution, to at least that part.
Generally speaking I think way to many services assume that they're allow to roam the filesystem freely, when chrooting should be "the bare minimum" one could expect.
Debian does this in the default installation, it uses capabilities I believe, not chroot, but the result is that there is a "white list" for directories where Redis can write, which are just /etc/redis/... to rewrite the config, and the dir where Redis persists.
Generally speaking I think way to many services assume that they're allow to roam the filesystem freely, when chrooting should be "the bare minimum" one could expect.