Originally Posted by
neocaligatio
... the semi circular cog attached to the thumb-bit doesn't engage the rest of the mechanism. ...
Oh, that's not good. At the top of your picture, there's a medium sized gear; it hides a smaller one, that it's attached to on the same spindle. That smaller gear is what the big semicircular one engages. The small one doesn't have many teeth, since it's small, so it's the first thing to wear out, in which case it may be that you're out of luck. But it's a fairly long gear, maybe 3 or even 5 mm long, and possibly it's only worn at one spot; so if you bend the semicircular gear up or down, it may engage the little gear at a spot where it's not worn.