Okay, so create_session requests are returning the NFS4ERR_DELAY error. This could indicate the server cannot accept any sessions, which could potentially be due to lack of resources (usually memory) on the server. This is specific to NFS v4, because it is a stateful protocol requiring the server to track some state for each client. In contrast, NFS v3 is a stateless protocol. The difference could explain why it works when NFS v4 does not.
You mentioned:
It might have to do with a move to NFSv4 mounts that I recently introduced.
The increased resource requirements on NFS server when using NFS v4 could explain the situation. What are the NFS server specs, resource-wise?
Any any rate, troubleshooting should now focus on the NFS server to determine why it is sending the delay message. Do you see any nfs or rpc related messages in journal/dmesg on NFS server side when this is happening?
EDIT: Can you also check that contents of /etc/machine-id is unique and different between all NFS clients?