You might use the fact that there are many who resell GoDaddy domains as evidence that they are widespread. That doesn't necessarily mean anything, but at least it says they seem to be popular for one reason or another.

A
Google search will find you a list of resellers. (You can tell it's a GoDaddy reseller by the
familiar co-branded look.)
I'm not sure what you're changing on you domain, but if it's DNS you need, there are many free and commercial DNS providers.
ZoneEdit,
XName,
EveryDNS, and
WorldWideDNS to name a few.
If he/she is shy of free services as most PHBs are, WorldWideDNS is a pay service. I think all of the providers I mentioned have redundent servers located in diverse locations (ZoneEdit and WWDNS does for sure). There are many others, you might try a "Similar Pages" search on Google.
My $.02