You have two options here:
Duplicating the old client.
An easy way to to this without messing around with permissions is to simply recreate the template target device and the initialization data you are storing in its dataports.
The spec command of Exoline's would be super useful to use here: https://github.com/exosite/exoline#spec. Spec will automate making the client's resources, so you will have to record/write the data back later.
Moving the client
If you do have access to the subdomain's root CIK you can you the RPC API to move just about anything anywhere in your One Platform client hierarchy(AKA your domain).