Is there a security advantage to using a different shell for the root account, either a hardened shell program, or simply a shell binary stored in a non-standard location?
Depends. If there's a different set of attacks that can replace
/bin/bash than some other files on your filesystem, then maybe there's a case for it. I used to make my root shell on Solaris a statically-linked
/bin/sh. The reason was that
/usr/lib was on a different physical disk than
/, so in single-user mode it might not be possible to start a dynamically-linked shell. The fact that this also avoided touching any compromised shared objects was merely a side-effect.
In other words, if
/bin/bash and your proposed alternative root shell are on the same partition, with similar permissions, there probably isn't much point. An attacker who can trojan one can trojan both.