" I would've thought you could simply set up your various DNS records in advance with the new service you use, and then switch the nameservers in the GoDaddy control panel."
Yes, see my comment.
"does anyone have any experience of using them?"
I don't but it wouldn't be a bad idea to setup other servers (as secondaries) at another provider. The only downside to this is that you are then susceptible to anything that happens at the extra provider (not if they don't answer or are down, but if your dns gets hacked there.) Keeping my previous statement in mind, if you are picking a reliable dns vendor I would say it probably pays to setup secondaries elsewhere for extra redundancy. It's not that expensive to do.
I don't but it wouldn't be a bad idea to setup other servers (as secondaries) at another provider.
Thanks, that hadn't occurred to me in the slightest. You're right that it's not expensive, and as a direct result of your advice, this is the road I'll be going down. Thanks!