Watch the first rep - watch the ends of the bar bouncing as you dip. All that extra movement is from you starting to dip too abruptly - your shoulders drop out from under the bar, so the bar falls on your shoulders. You need that bar to stay totally connected to your shoulders as you dip and drive, so control the acceleration down in the dip so that you don't lose that connection.
Not to be a ball breaker, but you're not getting the bar as high as it sounds like you think. You either need to get it higher, change directions to get under it more quickly, get lower in the split, or all three.
You're also a little forward. Think of driving the bar back over the back of the neck and reaching the front heel and hips forward - hips under the bar, not behind it.