It is obvious you are forcing the issue with your gear choices, you should be in the right gear in the first place without the need to change last second! You should NEVER put full force whilst changing down to a lower gear, the chain has to open up! to fit onto the bigger gear. How can it do this if your forcing the chain to stay on the current gear with all the force you have available. You are basically having a tug of war between the pedals and the shifter and therefore the chain breaks!! Add the increased forces of going up hill. I bet my house/car/savings/pension you wont/cant break a chain as a single speed setup. 😯