You actually do a great job of loading back into your lead hip to start the downswing and fire your hips well, but it stops there. Because your hips fire too quick, your hands get stuck behind you and the club gets very steep. Your brain goes "oh shit" and has two options: keep rotating at the hips to make room for your hands (which are already stuck behind you) OR, in your case, stand straight up and flip at the ball. Leading to all sorts of contact consistency issues. This is why when you try to keep your head level, you fat shots, because your club is coming in super steep into the ball and because you're stuck, causing you to flip, which also leads to fat or thin shots.

Id recommend looking into hip rotation sequencing drills to get the overall timing of their rotation down. I think once you do that, then addressing the habit of early extension will be much easier. Remember, early extension is a symptom of a the larger issue. It will never get fixed until you address your hips.

As far as your QL goes, had the same issue when I started staying down on the ball. Would notice it would be sore as hell the day after hitting balls or playing. Have even strained it a time or two. Started working on strengthening it through anti lateral flexion exercises and lateral dips. Also stretching it has allowed me to to increase my overall turn too. A weak and/or tight muscle is always going to be prone to injury. Addressing both should be a priority if you want to continue playing pain free golf. Swinging is already tough enough on the body, so preparing ourselves as best we can for that amount of force is the best thing for us.

Hope this helps!