*sigh*
The answer is that the large exported filesystem is a very large XFS...
and at least through CentOS 6, upstream has *never* fixed an NFS bug that
I find, googling, being complained about in '09: it gags on inodes > 32bit
(not sure if that's signed, or unsigned, but....).
The answer was to either create, or find an unneeded directory with a <
32bit inode, rename the high-number inode, move the new directory to that
name and location, move everything that was under the old high-inode dir
to under the new, low-number inode dir with the correct name, and
reexport; I restarted nfs for good measure, and all is right with the
world (well, after I restarted autofs and nfslock on the clients).
mark