1. Use your body to keep the bar close. The bar wants to be below your shoulders. during the scoop, your shoulders are moving from in front of/over the bar, to behind the bar. There's no reason the bar shouldn't be moving back into your body then - the only reason is if you're letting it pull you forward, stiff-arming it, etc. Just relax your arms and think of sliding the bar up your thighs once it's above your knees.
2. Use your legs to get under the bar, not your back. Back pain in the jerk is almost ALWAYS a result of locking the legs out prematurely and trying to squeeze in under the bar, which then happens through hyperextension of the lower back. So if you get the bar and your hips to the correct height, you'll be fine.
3. Close grip overhead squat. If you can't do that, keep trying.
CF warm-up isn't a warm-up. It's just a shitty workout. Try something more like this
before you start your bar warm-ups.