Re-wire inside the trackball, before the USB controller gets ahold of the signal from the optic boards. Each optic board has 4 wires coming from it: Red (+5volts), Black (ground), and either Yellow and Green, or Blue and Brown (or Blue and Purple, I forget whether Happ or Betson has the Purple, but it's one of those). Cut the yellow and green wires, and cross-wire them, so that the Yellow lead now connects to the Green lead's pin, and vice-versa. Repeat for the Blue and Brown. Done!
(Just remember to un-do it if you ever pull that unit from the upside-down panel before it gets installed someplace else.)