If both feet are on the ground when you are deemed to have already gather the ball, you can choose your pivot. (a) is needed because of the gather step in the NBA—but it’s just an application of (b)(3).

You still need to explain to me how, under your interpretation of the rules, a dribbling layup is not a travel. In a typical dribbling layup, the player leaves his pivot foot (the right foot, for a right-handed layup), then lands on his left, non-pivot foot, and then jumps for a layup. Travel?