It turns out that the immutable bit doesn't work all that well. A
better way is to make the entire Nix store a read-only bind mount,
i.e. by doing
$ mount --bind /nix/store /nix/store
$ mount -o remount,ro,bind /nix/store
(This would typically done in an early boot script, before anything
from /nix/store is used.)
Since Nix needs to be able to write to the Nix store, it now detects
if /nix/store is a read-only bind mount and then makes it writable in
a private mount namespace.