Yeah domain override would work - just make sure that unbound allows via ACL queries from the other site IP range.
Also keep in mind that if your looking for machineX, which might be machineX.sitea.tld, when it moves and gets a new dhcp lease in site b. You would want to find it via machineX.siteb.tld fqdn
If you setup your machines to use suffix search for both siteA.tld and siteB.tld would be possible for the user to just look for machineX