Sure enough, with the arrival of the VPC Stick and Base, a solution for my VKB issue was suggested on the VKB forums. Spoiler alert … it was previously hinted at here @wheelsup_cavu and @Wes.
At VKB’s direction, I disassembled the base again but this time, I went a step further. After loosening the stopper grub screw it was time to …
… pull the axis assembly apart. This made the whole center part come loose.
Next step? Time to apply some Loctite (Red). This was requested by VKB to stop the Y Axis from apparently spinning. The stopper grub is intended to do the same process but it keeps coming loose; it is a tiny grub that is tightened with a 1mm hex key and I could never, apparently, exert enough force without bending and warping the key itself. Don’t judge me or my arm strength 
Time to reassemble and let it sit for a couple of hours to set.
Later in the evening I connected everything back up, after disconnecting the VPC stick that I have yet to use, and using the VKB Config software: set the stick to default and calibrated it. The calibration went very, very smoothly (much smoother than it had been in recent memory) and the VKB Tester app displayed no anomalous behaviour as I attempted to reproduce the error. Nice!
I started X-Plane and re-flew the flight that opened my eyes to the issue to start with. A JRollon module that has no aileron trim, forcing me to keep the stick slightly left of centre for long periods of time. After two hours I can report that the issue did not show up.
Wooo!