Ah well, I figured I'd ask.
Further experimentation shows that I can get a reliable signal by raking the two contacts across common in rapid succession. Common C1->C2, or Common C2->C1 yield wheel up and wheel down. Unfortunately, I'm not a skilled enough electrical engineer to know how to simulate that effect without a rotary encoder.
For my hack, I'm just going to use the wheel up trick to get one key, and the wheel click to get a second key. Two keys will be a lot more useful than a single mousewheel that I never use, even if I'm technically "Losing" one key to the hack.