Domain registration location doesn’t matter. You are correct in thinking the nameservers are the end game
What you want is to fully host the mydomain.org domain.
If you go to view your domains, there should be a ‘deactivate mirror’ button for the domain. Click that and then add it as fully hosted. Make sure it points to the file location where you installed the dreamhosters account (/home/username/mydomain.dreamhosters.com in your case).
(FWIW, you should have added the domain in as mydomain.org, had it live in /home/username/mydomain.org, and had mydomain.dreamhosters.com mirror that. Then all you would do is change the nameservers and voila! )