I would say that the problem isn't a lack of sweeping the bar back toward your body - In fact, you sweep it back too much. The problem is that your hips move up HIGHER than your shoulders, which should never be the case, no matter how long your legs are. In the time it takes your hips to reach that position, the bar moves up maybe 3 inches.
You're in way too much of a hurry lifting from the floor - you can't snatch from the floor, you need to snatch from the upper thigh. The key is getting there with the right posture and balance so you can hit the gas and get the right result.
I agree w Josh's suggestion to practice snatch deadlifts to the knee with a slow separation from the floor. Focus on pushing with the legs and lifting your chest - make your goal to keep your shoulders directly above the bar until it reaches your knees, and not much farther over it as it pass the knees.
You do have very long legs and appear to be tall overall, which is going to unquestionably make this lift more difficult for you than for many others. Chip away at hip flexibility and back strength so you can get into a somewhat deeper-hipped starting position with a strong back arch and chest up. Lots of snatch deadlifts focusing on that upright posture - squat the weight up if it helps to think of it that way.
When you're snatching, slow down that first pull. Initially, I mean really slow - like count to 3 from the floor to mid-thigh, then without slowing down or pausing, explode into the actual snatch. As you get more consistent with the lift, begin bringing the speed back up toward a more natural pace, but you HAVE TO take it easy separating the bar - tighten up and push the legs through the floor rather than yanking it.