If we setup a ingress with MetalLB or Nginx, and added LoadBalancer into the template yaml, do you think this will work?

I would configure the k8s glue pod template to have "Service" port forward to the pod's 10022 port (default SSH port for the clearml-session), basically allowing the k8s ingest to allocate a port to the pod.
To test if it worked, spin the clearml session, and try to SSH to the external IP:port.
Once that works you can basically tell the clearml-session client which port/gateway it should ssh to