That plan will probably work. Make sure you have a way into both machines that isn't an interface like em0:1 (so no aliased interfaces). IPMI or a drac is even better. As soon as the new ip comes up run arping on the new machine to update the router and switches.
If you want to absolutely ensure this goes smoothly you should have a plan to remount the NFS mount on all the clients. Automating this sort of thing is generally really easy. Try using sshpass and ssh-agent. I'm not saying you're definitely going to have to do that, but its a very real possibility. I would also not use hard errors on an NFS mount, they make software lock up.
There's an alternate way of doing things. If you've figured out how to run a mount -o remount on all the clients, then you might as well consider changing the ip on all the clients. Its worth figuring out if it'll be smoother that way. The steps would be to stop any software using the directory with the NFS mount, change the ip in /etc/fstab, run mount -o remount /path/from/fstab, and if it mounts correctly restart the software. It'll take way longer that way, but your chances of failing to notice that one system is handling the change badly are way lower.