Best way to deal with domain mapping when changing servers

I have a multisite now on a shared server. I know I will need to switch to a dedicated server, as I am already having problems using too many CPU minutes.

But my question deals with domain mapping: many of my subsites are using the domain mapping plugin. I had to get a dedicated IP Address on my shared server for this plugin.

So when I move to a new dedicated server, I believe that I will have to go to a new IP Address. This will mean that all the subsites that have updated their A Records pointing to the old IP Address will no longer work. They will manually have to update their A Records with the new IP Address, right?

I am just wondering if someone has done this before and have determined any options to minimize the time that the subsites will be down, until they update their A Records. Are there any tricks to have their sites somehow forwarded to the new IP Address?

Thanks, Joe.