I'm an idiot. That's what happens when you spend your day totally rebuilding your server. You get dumb after 8 hours.
I was forgetting the "export" in the path. That fixed Kodi right up for me. Kodi still refuses to browse the server at the root level when I add the source in the GUI, but adding the source manually in sources.xml works perfectly.
I'm not sure if NFS is still the best solution for streaming in home these days, but my variety of Kodi boxes (openelec, nvidia shield, PCs, etc) all seem to agree on NFS so it's just easier.