To be honest I think I have it sorted. I think it has something to do with tolerances. The instructions specify fairly precise gaps so things run freely. A shaft on too acute an angle can prevent parts from moving/engaging. It actually works in a very similar fashion to a real-world dual range box.

I think I have it sorted but time will tell. The gearbox build was interesting. Pretty complicated. I have a post about it coming up. With images.