Does this work with Kubernetes image pulls?
You should be able to run unregistry as a standalone service on one of the nodes. Kubernetes uses containerd for storing images on nodes. So unregistry will expose the node's images as a registry. Then you should be able to run k8s deployments using 'unregistry.NAMESPACE:5000/image-name:tag' image. kubelets on other nodes will be pulling the image from unregistry.
You may want to take a look at https://spegel.dev/ which works similarly but was created specifically for Kubernetes.