Here is the problem; God's grace is conditional upon your correct choices, which means that it cannot be the grace that saves you. If you have to choose the grace, then your choice is the root and therefore cause of your salvation, not the grace itself. And faith, by your definition has to be a work; is it not something that you must do? If it is, not matter what you may want to call it, it is a work. So even if you say we choose faith, and then by faith grace, then we are still the root of our conversion, which is works righteousness.
So you believe in works righteousness?