After some six months of not getting around to having my graphics tablet repaired, and then finally sending it away only to be told there is nothing wrong with it, I have isolated the cause of its flakiness: A noisy power supply.
It turns out that simply using a different power point/outlet the problem disappears, so now I can draw like a normal person again!
Whether or not this development will be a positive thing for the future of Willy & Dalbert et al, remains to be seen – Here you can see my first attempt to draw them by hand [admittedly fairly roughly].