Probably the easiest thing to do would be to use the "resiliency" list on MBG to program the new IP address that you will be receiving in the future along with the current IP address of MBG. This will be sent to the sets that connect as "persistent" addresses, IP's to try after a set re-boots.
That way, when you do switch providers, the set will attempt the old address, fail, then try the new address and succeed.
When MBG is moved to the new address, configure the resiliency address to only be the new address.
This is under the clustering->resiliency panel.