Christopher Caldwell writes:
Why don't you slowly decrease the TTL on your name server until you're ready
to renumber. Configure your web server bind to the old address(es) and new
address(es). Re-number in the DNS, and your customers will experience
something like no down time. Then put the TTL back to where it normally is.
I've run customers dual addressed during transitions. It has the
advantage of eliminating downtime, and the disadvantage of requiring a
bit more labor to do the move in two phases.