Can you say more about what you did with EBS? It seems like it would be necessary to make some compromises in availability and disaster recovery because any given EBS volume is restricted to the availability zone where it was created.
We were hosting third party software in an EKS cluster and needed a way to share state between components of this system. We tried EFS initially but it actually killed the EKS cluster with iowait under load. We found a way to divert most of the systems requirements to local emptydir volumes, leaving only infrequently accessed media files on EFS