A bit more testing. So... newer driver again and I adjusted settings in the NVidia control panel:

FFXIV - 3D Management - VSync - Use application setting (it WAS turned to always on)
NVidia Control Panel - GSync On for my monitor (60hz refresh rate on my 4k monitor)
FFXIV - In game system setting - FPS Limit to 60 - so far no stutter in Eureka fights (generally fights with lots of flashes of magic and explosions would make the issue happen immediately)

I'm going to try no FPS limit later and see what happens. Perhaps it was VSync and GSync fighting, but I'm not sure why the driver prior to 3/28/18 didn't have the problem, but newer ones do.