I took the coil, circuit and battery from an Artwizz module made for the MM and installed them in the mouse. A piece of plastic from a floppy disk covers the coil and the hole. The floppy wasn't quite as yellowed as the mouse, but close enough!
I've also played around with the MM settings in BetterTouchTool, like ignore zones and pressure thresholds. Using the mouse now is much more intuitive, and honestly really pleasant!
An unintended extra feature is setting the click pressure by twisting the torn off cable stump!
Up next is to modify the wireless charger into something more... suiting.