Some ideas:
1. You could just add a nameserver. There's no rule that says you have to have exactly two. You could almost certainly have three. (There are some registry-specific rules that specify the minimum and maximum numbers, but I've never seen a registry where the maximum was two.) If you add a new nameserver, and leave your existing two as they are, you've achieved your diversity goal and avoided the problem you're currently struggling with. Apply a touch of mind bleach, and you'll forget that "glue records" are even a thing.
Unfortunately, I have other customer hosted domains and they also are listed only with 'ns1' and 'ns2' of my domain, therefore, if there is an outage, unless I can actually update the ip of 'ns2' to my new off-network host, those other domains are still a fail. Changing the ip of the host is the right answer in this situation.
So those are the people I would ask to rename (say) NS3.P23.DYNECT.NET. Of course in this case they would say "haha, no" and probably advise me to add a nameserver rather than trying to reconfigure their commercial DNS service. But you get the idea; if the nameserver you want to rename is subordinate to a domain name you have administrative control over, you could interact with the registrar for the domain and make the change.
The precise way a particular registrar will accept such a change varies by registrar. Sometimes (I hear) the user interface involves phone calls and shouting. But then you have a choice of registrar, if you can figure out how to make transfers work.
This seems to be the case with dotster. I apologise to anyone over there who may be reading, but it seems that they are completely clueless. They've told me again in support they affected the change, but I can see that all they did was update their own customer hosting account zone data and not actually push it out to the roots (or more correctly the gtld's?).
If your domain and/or nameservers are not named under NET, ORG or COM, the above may be useful or, quite possibly, completely irrelevant, depending on factors that your registrar is in theory supposed to hide from you. There are as many other data models as there are other TLDs, almost-maybe, and I certainly don't know the details of all or even many of them.
If this is sounding very XKCD-927, that's because it is. This is perhaps why lots of people pay others to do this for them (registry/registrar shenanigans and DNS hosting) so that they can live their lives with one less thing to be angry about.
So what I need is a registrar with a clue about the glue... Open to suggestions here... Mike-