Minor update:
Since the transponder wasn't getting detected while mounted vertically, I tried rotating it 90 degrees so that now it was horizontal, but still in the same location to the right of the camera. It appears to have worked, since I was not charged the one time I drove 237E while it was set to 2 people.
So I can only assume my problem was with the orientation and not the location. Seems like these new candy bar style transponders only work if they are horizontal. Maybe the signal they emit is directional.