Your knees are forward enough and your torso upright enough in the first frame so I imagine your descent is okay. The problem is that your knees shoot back too fast too soon and your hips shoot back and up. Some cues while you back squat that can help is think rigid shins and knees and really punch your hips forward.
Your back angle shouldn't be that much closer to parallel to the ground than from the first frame. Now even in the most technically proficient squatters, the back angle does become a little closer to parallel to ground but no not to that degree even in a great squatter that uses a lot of back. And no one tries to emphasize it. In fact, people try to de-emphasize doing that.
If you're even doing this with front squats, maybe you need something even more remedial. Goblet squats can be good in this regard. It's even harder to turn that into a good morning. You could do practice sets at home, as part of a warm up, and as a finisher. And you can use them for working sets during your training session too.
The OH squat idea isn't bad at all either. And you might actually need to do some really direct quad work like you mentioned if the issue is so back you do it on front squats too.