Switch ingress controller to new static IP with zero downtime?

Question

My AKS app uses a standard ingress-nginx ingress controller with a static IP, installed via Helm chart:

myStaticIp=1.2.3.4
myNodeRg=MC_foobar_eastus
helm upgrade --install ingress-nginx ingress-nginx 

  --repo https://kubernetes.github.io/ingress-nginx 

  --namespace ingress-nginx --create-namespace 

  --set controller.ingressClassResource.default=true 

  --set controller.service.loadBalancerIP=$myStaticIp 

  --set controller.service.annotations.service.beta.kubernetes.io/azure-load-balancer-resource-group=$myNodeRg

How can I cut over to a different static IP with zero downtime?

Updating in-place and re-running the snippet above would update the ingress controller, but users would experience a downtime during the DNS caching period.

I suppose one option is to create a second ingress controller with loadBalancerIP=<newIp>, otherwise identical, and clean up the old one after the DNS caching window.

Just curious if there's a better way? Maybe something like a rolling update over multiple days?