Well, adding a largish (1000uF) capacitor to the 3.3V pin seems to have helped a lot.

Not perfect, mind you -- I can still trigger a reset of the USB chip with repeated stressing of the motor, but this is much harder to achieve than before.

I'll add a 0.01uF ceramic alongside the larger one when I transfer the design from the plug board to a soldered product.

Cheers