Another update... I checked out the "new" error, and found mention on the web that it could be related to having to refresh the displaying of datastores in the vSphere Client to show datastores that happen to be "hidden" for some reason. Well, when I pushed the damn "refresh" button, I suddenly saw ALL NFS datastores appear. 
So it looks like that particular error is no longer a mystery: they EXISTED so ov-bviously couldn't be re-created.
After 2 complete ESXi host shutdowns and some NFS server service restarts on the 2012R2 server, the NFS datastores seem to retain connectivity for now. A "refresh" doesn't even seem to be absolutely required to have them displayed in the vSphere Client.
Still doesn't explain the first error, so just keeping my fingers crossed...