Right now if you want to first migrate your configuration and in a second run your websites it's not possible.

Why?
Because in your second run, you will set in Configuration.groovy all the modules to migrate to false and you will provide no "custom" module to migrate.
And then Configuration.getModulesForIDCreation will return an empty list.

This list is needed by the migration of your websites.
In ConfiguredMigration.groovy, this list is needed to create the list of pages ID and components ID used by your website. So if this this is empty, the templates information wont be updated in the content of your websites.

How to solve that:
Configuration must be improved. As for the modules, we must define the templatingDependency of a website, and then according to that update the method Configuration.getModulesForIDCreation.