Multiple Ingress controllers in Kubernetes
I assume you've created your nginx ingress controller in it's own namespace? By default it's called ingress-nginx.

You can create your second Nginx Ingress controller in a seperate namespace so that it's logically isolated from your first. You'll need to give it a different name, but I see no reason why you can't do that.

Doing so will spin up a seperate AWS ELB, which you can then map to your new DNS record and then you can slowly migrate your services over.