So the latest kernel for Ubuntu 14.04 LTS (4.4.0-116) completely borks the Nvidia binary driver. Following installation of the latest round of system updates today, my displays were completely hosed. Main display at wrong resolution, and secondary/tertiary displays completely inoperable.
Tried reinstalling the binary driver from the Ubuntu repo, and also tried using Nvidia's own installer. No dice. Looks like the system was failing to load the binary driver, and falling back to the Open Source Noveau driver (which apparently does not get along with my GT 720).
Backed off to the 4.4.0-112 kernel and everything works again. I'll try the next kernel they push out (whenever that happens) to see if they've got the issue addressed.
I suppose I really ought to get onto a more modern version of Ubuntu. I had meant to upgrade to 16.04 LTS at some point, but now that 18.04 LTS is just around the corner I'm inclined to wait.