BTW: I've solved the issue.
It turns out that I had been choosing the wrong input device with reconfiguring xserver-xorg.
I was choosing /dev/psaux rather than /dev/input/mice.
And therefore it was choosing completely the wrong type of mouse.
I reconfigured xserver-xorg and chose the proper
setting for my mouse and it all works correctly.
This has turned out to be a major case of PEBKAC, and I really need to stop attempting to work until one in the morning.
But those remapping tutorials may still come in handy.