IMO, the deadlift has two phases:
1) Floor to just above knees. In this phase the back angle should remain static (the one you showed at the start is pretty good). All of the movement should be knee extension; think about pushing the floor down and dragging the bar across the shins. This is all vertical.
In this phase, the quads are the prime mover and the glutes/hamstrings anchor the pelvis in place isometrically.
2) Knees to lockout. In this phase, the movement comes from hip extension. The legs should almost be locked out here, and the movement comes from bringing the hips forward to meet the bar. This is more "horizontal," if that makes sense.
In this phase, the glutes and hamstrings become the prime movers.
You are essentially neglecting the first phase and relying exclusively on hip extension. This is a pretty common mistake and, IMO, results from not having sufficient static strength in your glutes and hamstrings to allow you to hold the isometric while your quads break the bar from the floor. As such, you will need to lower the weight and really concentrate on the first part of the pull from the floor to knees.
As Tedro said, the hip angle you show at the start (when the bar is on the floor) is pretty good actually. I'd focus on holding that angle as you break it from the floor with the legs. Good luck.