After a week of running faultlessly, the Plex server decided it didn't want to do NFS properly. I could list the contents of the mounted shares, but not the contents of any files. I could still delete files, but not create them. And even more oddly, out of the three mounted NFS shares, one still worked perfectly even though the configuration was identical.
Anyway, after rebuilding the Plex server from scratch and perfectly reproducing the problem, I fixed it on a hunch by changing the mount type from nfs to nfs4. It looks for some reason like the Plex server was defaulting to nfs3 - which won't work because I haven't enabled statd. I haven't seen that behaviour on any of the other mint/ubuntu boxen, so I'm figuring it something to do with the Plex server being virtualised (using kvm/libvirt) and accessing shares from it's own NFS host.
I did try using virtio/virtfs to give the Plex server direct access to the shares on the host, but that doesn't play nice with ZFS.