First off, the logitech mouse I used apparently had it's 'back' and 'forward' buttons emitting 'mouse button 4' and 'mouse button 5', while the Kensington trackball is emitting 'middle mouse button' and 'mouse button 4'.
To rectify this, I found X-Mouse Button Control. Using the 'Simulated Keys' option, I mapped 'Middle button' to 'Mouse Button 4' and 'Mouse Button 4' to 'Mouse Button 5'. Thus, I get my back and forward buttons where I want them on the trackball.
I suspect that if I had other mouse-type devices plugged in at the same time, I might not be happy with the result, but since I'm only using the trackball right now, it works fine.