Changing Nameservers - No Downtime (How do registrars do it)?

I have a domain name: abc.com
It is registered at registrar.com and uses their nameservers:
ns1.registrar.com
ns2.registrar.com

I just got my own DNS server up and running. Works, tested on some new domains. I want to switch the nameserver away from my registrar to my nameservers:
ns1.mydns.com
ns2.mydns.com

Now, I know when I have transferred domains from one registrar to another, it has happened seemlessly. The new registrar takes over the DNS duties and yet there is no downtime.

I am trying to do this same thing but it is not working. Here is what I did:
Plan A

1.) Change nameservers at registrar to ns1.mydns.com and ns2.mydns.com

2.) Add a new zone to my DNS server

3.) Add A and MX records to my DNS server

There is downtime. I am guessing this downtime is due to the new DNS records getting propogated. I have a TTL of 2 minutes of my records but since they are new records from a new zone, I am assuming the first time around takes some time to propogate.

So that brings me to theoretical plan B...
Plan B

1.) Add a new zone to my DNS server

2.) Add A and MX record to my DNS server

3.) Wait a few days for propogation

4.) Change nameservers at registrar to ns1.mydns.com and ns2.mydns.com

Now the problem I have with that theory is I can't see the new DNS entries propogating anywhere wihle the nameserver is still ns1.registrar.com and not ns1.mydns.com. Otherwise, some moron could make millions of fake DNS entries on a DNS server with a short TTL and just clog bandwidth with worthless propogation.

So, how do registrars transfer nameservers from ns1.registrarA.com to ns1.registrarB.com (from one registrar to another registrar) with no downtime?