I've been hosting with another company for quite a while now, and their name servers have been configured to resolve an elaborated set of names to my server. I will be migrating services slowly towards my new SM server, but don't want DNS to be interrupted for a long time during the in-transit period (which might last for a month or so) - especially for the services which I'll keep on my old server until the new one is set up correctly.
For having access to Orbit's DNS panel, it seems like this is an all-or-nothing approach: there's a check whether ns1.servermatrix.com is the primary DNS for all of my domains, which it won't be during transitioning. I'd like to start with only bits and and pieces for the time to come.
How should I do this in the least disruptive way?
Another clueless SM newbie question: are we supposed to run a DNS server on our own servers, or do we get access to SM DNS servers?

You have an option here, you can use SM DNS or set up your own. For me, I used SM DNS because I am not reselling web accounts. For those who are, hosting their own DNS might be a good idea as it gives them control and some separation from the datacenter.

What you could do in your case would be to set up your sites on your server here in SM and during the transitional period keep the server here and the one you are transferring from active for the next 72 hours for the DNS to propagate. Once you are certain that the server here is nicely configured, change the DNS server entry in the Domain Name registrar for the sites you are moving to point to the one which works here. So during the propagation time, you will get some people reaching the old and some the new machine but since both are active, there would not seems like any downtime in that respect.

During the transition, you can move all or one site at a time. I would suggest doing it to one or two first then when you are sure that it works then move the rest.

The tricky things would be Email and Database. Emails would probably reach both on the new and old machine so you might want to access the mail servers via IP address as POP3 server during the transitional period. Do that for the new and old machine. As for database, it would be the same thing.. if they reach the new machine, it would post to the new database and if they get to the old, they will post to the old database. You may want to change the IP address to point to the new machine database.

For the most parts, no one would even notice the transition.