We're integrating with a new partner that requires us to use VPN when communicating with them (over HTTPS). We're running all of our services in a (non-private) Google Kubernetes Engine (GKE) cluster and it's only a single pod that needs to communicate with the partner's API.
The problem we face is that our partner's VPN provider won't allow us to use the private IP-range provided by GKE, 10.244.0.0/14, because the subnet is too large.
Preferably, we don't want to deploy something outside our GKE cluster, like a Compute Engine instance, that is somehow used to proxy our traffic (we will of course do it if this is the only/best way to proceed). We're hoping that, perhaps, it'll be possible to create a new node pool in the same cluster with a different (smaller) subnet, but so far we haven't found a way to do this. We've also looked briefly at CloudVPN, but if we understand it correctly, it only works with private GKE clusters.
Question:
What's the recommended way to obtain a smaller subnet/IP-range for a pod in an existing (public) GKE cluster to allow it to communicate with a third-party API over VPN?