I’d suggest another workflow: select all events and delete them, also delete track versions in case you’ve used them. Use ‘backup to new folder’ (remove unused ticked). Now you have all tracks/groups/fx set with no events in you project window (verify this from the pool, there shouldn’t be anything shown there). Drag and drop the events from an unmixed project into this template. Repeat as often as needed.
Be careful though, removing events from the project window means, they are still referenced in the pool. In case you choose to delete stuff from the pool the original files will be deleted with no chance to bring them back!
There’s also a relatively young function called “Import from project”. Could be useful for your case as you can choose which track should go to which track. It seems to have some flaws with media files not always getting imported though this option is ticked. Rechecking the pool (and perhaps manually tell Cubase to archive them to the projects audio folder) may also be a great idea here.