Success! I got it working finally. It was just as I suspected. I wound the belt the wrong way around the drum.
I think what confused me was that in the document it says the spring takes up slack in the cable. This isn't actually the case. The spring just forces the drum back to its home position. If you set it up so the spring takes up slack in the cable, you risk the tension in the spring + the drag in the cable overwhelming the spring on the throttle plate. If this happens, the throttle won't close and you get taken for a ride.
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