I think most of the issue is in your takeaway, which is the part of the swing starting at address and ending when the club is parallel to the ground (when the club head is hand height). Looking at the target-line view (view from behind you as you swing), watch the video frame by frame (I did it just by pressing spacebar twice really quickly to "play-pause" the view to allow about a 10th-5th of a second go by. Try to freeze it right at the end of the takeaway. First off the video is slightly off alignment. You want the video to be on the line parallel to the line connecting the ball and the target that passed through your hands (so parallel to the target line but about a foot closer to your hips). Even so, you can still see for the most part what your issue is.
At the end of the takeaway, you want the clubface to be such that it is basically blocking the view of your hands. In your video, the club face is WAY to the left of where it should be (outside of even your hips). Some of this is caused by the video not being perfectly aligned, but even if it were, you would still have an issue. Because you have the club so inside to out on the way back, you are trying to correct for it by going outside to in on the way back. On the way back if you look at where the club head is when it is parallel to the ground you can now see it is on the other side of your hands (it should once again be such that it blocks out your hands when viewed from the correct angle). You can even see the club bow concave toward you. The outside to in swing path will cause a slice.
I believe the issue is you don't have a one piece takeaway. That is, you are turning your shoulder and hips too early in your back swing which brings your club off plane (too far behind it). Your takeaway (again the part of the swing from address to club-parallel-to-ground) should pretty much be all shoulders, like you were swinging a putter (don't confuse this with upper body shoulder rotation, rather just use your shoulders to raise your clubhead away from the ball). Also try not to break your wrists early like you are doing. The takeaway should be 90% shoulders moving the clubhead away and 10% wrist break. The wrist break should happen just at the very end of the takeaway to slowly being to rotate your clubface open and level the club. No hips, no torso rotation.
A good way to practice this is with a mirror. Put a mirror behind you and practice just the takeaway. It should feel almost like you are swinging a putter over and over (admittedly a much longer stroke). At the end of the takeaway check and see that your clubhead is blocking your hands in the reflection. Alternatively you can have a friend stand behind you and check. Make sure either your friend or the mirror is aligned correctly (same as where I said the camera should be). As you practice the takeaway start to add on the rest of the swing until it feels natural. It may take a long time to develop the muscle memory. Likely if you fix the issues int he takeaway it will help fix the over-correcting you are doing on the downswing which is producing an out to in move that gives you the slice. I remember I spent a week at one point going to the range and hitting 50 balls a day with JUST a takeaway. I would take 3 practice swings where I checked my clubhead at the end of the takeaway then I would pitch the ball doing just a takeaway. I did this just to build that muscle memory of getting the clubhead in the right spot because building a good swingpath is so important.
Just as an aside--I in general think a one plane swing is much easier, but even if you use a two plane swing, the clubhead should pass through the points in the takeaway I described. For example, Jim Furyk, who has a really weird swing with I guess you would call two planes:
you can see if you look at 0:41 and 1:00 that in his backswing and downswing his clubhead blocks out his hands. On the way down (at 1:00) his club is actually a little INSIDE his hands meaning he has a slight IN to OUT swingpath which will produce a gentle draw (whereas your severe out to in swing is going to produce a wicked slice). I have heard it mostly suggested that your swing, especially with a driver, should be very slightly in to out as Furyks is here.