The leftward slide of the hips is of the hips only, not the upper body. AND the slide is not a very large movement: could be somewhere total between 3 and 6 inches...but it DOES move the weight left. OTT is for the reason that you TURN your shoulders around instead of TILT the right shoulder down. If you stand looking in a mirror and move your left hip left leaving your head stationary, your right shoulder DOES move down. It is structural..not independent of the left hip and spine motion leftwards. There is no reason at the BEGINNING of the downswing for the shoulders to TURN; that comes later.
If you shoot a gun with a 6" barrel, the direction of the bullet is already committed by the direction of that first six inches. If you make a downswing with a left hip bump and a right shoulder movement down, you have committed the swing on plane and if truly your weight DOES move left, you can NOT swing over the top.
This is a maxim that will help enormously: Wherever your weight is located, THAT is where your body rotation will occur. So if you are still standing mostly on your right foot, your body will swing around a piano hinge running up your right leg. If you are standing on your LEFT foot, your body will rotate around your LEFT leg. Wherever you are balanced - if it is in the middle between both feet also - your pivot will rotate around THAT.
A pivot around weight centered between BOTH feet is totally powerless. ALL good swings have the majority of the weight on the left heel at impact: some go to that heel earlier than others, but none succeed that don't get there.