You're doing a good job keeping the intensity up--keeping the bar in motion and not wasting time--for the whole set. However, as a result, you're rushing through lockout. Think "higher, higher, higher," and get it as high as you can, every time.
Your back rounded at the end of your set. That's probably the cause of your discomfort. If you learn to thrust your hips forward to initiate the press, you'll lay back by hinging at your hips instead of overextending your back. They call it "Press 2.0" 'round these parts. If you decide you want to learn this technique, then there are good learning resources elsewhere on this site. I recommend getting some in-person coaching eventually, too.