Pardon the weird question:
Is the DNS service authoritative or recursive? If auth, you can solve this a few ways, either by giving the DNS name people point to multiple AAAA (and A) records pointing at a diverse set of instances.
Authoritative. But, also not the only thing that we are running that needs some geographic and route diversity.
DNS is designed to work around a host being down. Same goes for MX and several other services. While it may make the service slightly slower, it's certainly not the end of the world.
Oh, how I wish this were true in practice. If I had a dollar for every time we had serious issues because one of a few authoritative DNS servers was not responding... OK, I wouldn't be rich, but this happens all the time. Caching servers out on the net get a "non-answer" because the server they chose to ask was down, and it caches that. They shouldn't do that, but they do, and there's nothing that can be done about it. -Randy