OK, the mouse stuff seems to be working with overscan, now, which is good.
Additionally, the Game Controller code appears to be kinda ok.

I've set up the engine/framework/etc to assume all controllers are "The player's input", so I'm going to be doing 1-player only stuff until I can be bothered to faff about with it some more and implement multiplayer controller code!

Unfortunately, I don't 100% trust what GLFW3 is telling me.
The controller input list here is suggesting that DPad Up is "button #11", whilst my X360 pad is returning true for "button #10" whenever DPad Up is pressed.

I'll have to try a variety of controllers, I think, and try to figure out how best to handle the different types.

Worryingly, it might even be Win10, or the driver code, which is giving the incorrect result.
Arrgh.