What you're looking for is a serverless network endpoint group. Unfortunately, serverless negs are not shareable cross project.
It seems that you're already achieving cross project endpoint sharing via the internet neg. So in order to remove the fully qualified domain name from your neg you'll probably need to create a load balancer in the cloud run project and have your other load balancer point to it and then attach the cloud run instance via a serverless neg to that load balancer.