My question is: Is this even possible? All the documentation for HA that I've found appears to not do this. Am I missing something?
You can use oVirt for that (www.ovirt.org). For that small number of hosts, you would probably want to use the "hosted engine" architecture to co-locate the management engine on the same hypervisor hosts. It is included by the CentOS virtualization SIG, so on CentOS it is just a couple of 'yum install's away...
HTH,