Can you post a screenshot of the error you get? If you were to run webgisdr.bat -c -f webgisdr.properties to get the configuration of the deployment, does everything look correct?
The DR tool will simply check the federated servers of the site associated with the PORTAL_ADMIN_URL value via Portaladmin, so I can't see how it's picking up an incorrect URL for the services URL.
The DR tool can be used for this "full" migration workflow, but another approach is to create multi-machine sites/HA sites out of all of the components, and then remove the old machines. For example:
1) Move the config-store and directories for the Server to a shared location
2) Join the new machine
3) Remove the old machine from the site
4) Update the paths to the config-store and directories if necessary
5) Update the admin URL for the federated Server within the Sharing API
You can do the same thing for the Portal and Data Store. Create an HA Portal and HA Data Store and remove the old machines.
This is more of a "piecemeal" approach.