In Google Kubernetes Engine, is it possible to load balance over regions when using a custom ingress controller (e.g. ingress-nginx) instead of ingress-gce? How would that be done?
Technically, yes you could load balance across regions with a custom load balancer. It would depend on your intended purpose for the load balancing, as in: for internal or external traffic origins. There is a community doc for enabling nginx ingress for GKE. Some additional context and commands for nginx on GKE can be found on the Kubernetes github, nginx section.
Something to bear in mind is that Kubernetes clusters do not span multiple regions. So you would be load balancing (in the example of external traffic) between disparate clusters in different regions. Even if the clusters are running the same application(s), it will not be the same instance of that application.