I was unable to reproduce the issue with a single monitor, though I only attempted to do so for a brief period. I am already using the latest available graphics drivers ("GeForce Game Ready Driver Version: 452.06").

In the meantime, I seem to have resolved the issue by disabling the "System Configuration" -> "Display Settings" -> "Limit FPS when away from keyboard." option. After disabling this option I left the client on for 3 days straight, constantly switching back and forth between windows, watching fullscreen videos, dragging things over the FFXIV window, etc. and have not seen any further stuttering. I'll let you know if that changes.

In researching this issue I discovered that many people over the years have been having issues with the framerate-limiting options in this game. I suspect there may be some defective code somewhere in the client which relates to those features.