its not the transmission you cant put the gears in a rush in backwards or anything to make it run backwards. i own a rush and have replaced the diff cups, diff inner gears multiple times, stripped the centre gear in the gearbox and it doesnt matter which direction any of the gears are put in the car will still go forwards.(its impossible to put the inner diff gears in backwards they wont fit)

i agree with nitrofan your probly running rich thats why car is stalling. do you flood the motor a lot and is a lot of liquid pouring out the exhaust?