Proper way to add secondary DNS to public zone?
 

Yesterday the hosting provider (lets call them HOSTINGPROVIDER.com) that hosts the website and public DNS for the school (I'll call it SCHOOL.org) I work at was completely out. As a result, no one could send us email or use our other on-campus-hosted services. My boss told me "don't let this happen again".

I've set up a secondary DNS server here on campus, and it's doing the zone transfer just fine. What I haven't done yet, and am a little afraid to do lest I take our DNS down again, is alter our DNS servers at our registrar.

How do I add the new server into the pool without creating a circular reference? The software at the registrar won't let me add an IP address.

Right now our DNS servers are ns1.HOSTINGPROVIDER.com and ns2.HOSTINGPROVIDER.com. If I create ns1.SCHOOL.org and set that as one of our servers both at our registrar and in the zone (ie, IN NS ns1.SCHOOL.org), how does that actually get resolved if ns1.HOSTINGPROVIDER.com and ns2.HOSTINGPROVIDER.com go down?

To make it a little clearer, here is the relevant part of the existing zonefile:
And here's what I'd like it to be:

But what do I put in the domain registration for SCHOOL.org to make it work?

http://faq.domainmonster.com/dns/glue_record/ seems to suggest that what I want to do is correct, and that the registrar will take care of the recursion problem automagically.

Is this correct?