the mercy of latency time to google's or OpenDNS' nameservers
You won't usually need to worry about that. 8.8.8.8 and I now strongly suspect the opendns ones as well are Anycast addresses. There are multiple servers round the world that all have the same address. Fairly astonishingly (to me) this just works. No special provision has to be made other than of course advertising the address as usual into the internet from each site.
From the UK.
Reply from 208.67.222.222: bytes=32 time=19ms
Reply from 8.8.8.8: bytes=32 time=18ms
As a reference, a ping from the UK to new York has a round trip time of about 80ms so an instance of each of these these servers are quite close.