Hi Vince,
You don’t need to do any data plane level movements here: just add your new domain users to your Atlas org and then remove the old ones: and Org Owner level user can do this.
By the way, you can also move projects between orgs if you’re an org owner of both the source and destination org!
If you really do need to move a cluster to a different project/org for some reason: then the best bet is to use Live Migration, but that doesn’t seem needed in your case
Cheers
-Andrew