Dump the rendered window pixels out to a simple viewer. Mouse movement is still a pain to deal with, but I would default to spoofing it as moving between clicks, with some image parsing logic to identify menu traversal.
Then it should reboot the browser process regularly.
I've been waiting for someone to make a packaged 'VPC in a box' incorporating networking and linked VMs.
connects Chrome to a Tor SOCKS proxy and wraps all other browsing-related network calls over torsocks. It prevents local fingerprinting leaks (like this IndexedDB ordering bug) because the browser isn't running locally at all. You can host the BrowserBox instance as an onion hidden service, use it to browse over Tor, or both.
If you want to try an ephemeral "VPC in a box" style setup where the environment is destroyed after you're done, you can easily spin it up using this new GitHub action: https://github.com/marketplace/actions/browserbox (but you need a license key, obtainable at https://browserbox.io)
This is my attempt to make it easy to spin up bbx on ephemeral infrastructure that's mostly free (GitHub Actions runners are perfect).
Just use a network namespace individual pieces of software are way too easy to misconfigure.