You can set up a complete back-end with Instances having only internal IP's.
The tutorial you linked to doesn't specify if the back-end instances can work without external IP but they actually can.
After you set up everything and confirm it's working just edit each instance and set "external IP" to none (you may use gcloud
for this) - it will work as before. I just went step-by-step with the tutorial and checked if it's working - every instance was responding. Then removed external IP's and checked egain - also no issues.
Try going once again over the tutorial (try gcloud
this time - just copy-paste everything) and if it's doesn't work then put some logs / error messages in your original post and I will try to troubleshoot this.