So I'm working on a project that involves managing many postgres instances inside of a k8s cluster. Each instance is managed using a Stateful Set with a Service for network communication. I need to expose each Service to the public internet via DNS on port 5432. 
The most natural approach here is to use the k8s Load Balancer resource and something like external dns to dynamically map a DNS name to a load balancer endpoint. This is great for many types of services, but for databases there is one massive limitation: the idle connection timeout. AWS ELBs have a maximum idle timeout limit of 4000 seconds. There are many long running analytical queries/transactions that easily exceed that amount of time, not to mention potentially long-running operations like pg_restore. 
So I need some kind of solution that allows me to work around the limitations of Load Balancers. Node IPs are out of the question since I will need port 5432 exposed for every single postgres instance in the cluster. Ingress also seems less than ideal since it's a layer 7 proxy that only supports HTTP/HTTPS. I've seen workarounds with nginx-ingress involving some configmap chicanery, but I'm a little worried about committing to hacks like that for a large project. ExternalName is intriguing but even if I can find better documentation on it I think it may end up having similar limitations as NodeIP. 
Any suggestions would be greatly appreciated.