Re-addressing GTM during hardware migration

Code level 11.4.1 HF2 (not upgrading code, just migrating hw)

I will be migrating off 1600's to 2000S devices for our GTM devices (we have 2 datacenters, 1 GTM per). They are currently on IP space that will not be available when I bring over the UCS file to the 2000S devices. I can handle all the load errors etc, my question is - how do I eliminate downtime? Obviously our GTM's are very important and maintain DNS records for all major applications.

I have the new IP addresses picked out (listeners and under Servers new IP), and my plan was to do 1 GTM at a time - I'm assuming I'll need to do an gtm_add for the devices to grab their new IP's - correct? And during this process will DNS still work? Not sure if anyone has ever done this before, just trying to get some advice to limit any downtime.

Thanks!