An update (parts are from an e-mail I sent Andy):
Friday I received the new minipac encoder in the mail. When I opened the package, I noticed immediately that something was different with the encoder and rushed to get the broken one. Sure enough, when I looked at them side-by-side, the new one had a small orange part on it the other didn't: maybe a capacitor or diode of some kind? It was a slightly bulging orange disc with two metal legs that attached to the board. When I looked at the first/broken one, there were little solder points for the same thing but no component.
I plugged the new board into the PC for the cab and right away XP saw it and said, among other things, it was a "composite device", a "trackball", and so on. The hardware manager had it listed at a composite device. A quick connection to the panel showed it worked perfectly. The spinner worked nicely, and because the trackball was connected separately to the PS/2 mouse port, I could use the trackball or the spinner freely. I ran a pilot test of the panel, briefly trying Ms. Pac Man, Arkanoid, and Cyberball. All ran perfectly.
I never did find the missing piece from the first board and I was pretty meticulous with how I handled everything. However, now that all's said and done, the minipac is exactly what I needed and I'm very happy with it.