For zero downtime:
After everything works at DreamHost.
If the sites are already propagated with data, I’d use a HOSTS hack to get everything set up correctly on a Fully Hosted domain here. Another alternative is lower on that same page - using DreamHosts DNS from your local computer.
After you’re done, revert your local settings.
Yes, change them as a final check that everything is working as it should be at their new home. After that you can initiate transfer.
If your clients have active email, don’t forget to set that up before flipping nameservers too.