Currently, docker exec (somehow safely) fully enters the container's namespaces and cgroups, then exec's a command inside the container. My suggestion was basically to have a statically compiled C binary that executes in the fully untrusted context, which things can ptrace and manipulate all they want. The thought was that the C binary would open the file descriptor from inside the untrusted context so that it is incapable of doing anything privileged and then send the file descriptor back over the inherited unix socket via sendfd. I'd imagine the only way this could be vulnerable is if sendfd is vulnerable somehow since this means 100% of the path resolution happens from a fully isolated context.
The performance argument makes plenty of sense, but it sounds like it'd be solvable by just doing a classic tar pipe where tar (or similar) is running in the fully untrusted context and writing its output to a pipe (with no unix sockets involved). You'd just need to get that statically compiled tar binary into the container, similar to how `/dev/init` is done. Would this be unreasonable? `kubectl cp` is already doing an actual tar pipe via docker exec, the missing bit is that it fails if tar does not exist inside the container, so you'd need to inject it in. This would fully removed the complexity of chrootarchive and any path checking, and you'd be able to rely entirely on the security constraints of docker exec.