you've brought up several things to discuss.
1) How are you moving the weight up to set up for squats. If you are lifting only with your arms (like an upright row) and then trying to move it over your head, try instead to lift the weight up like a weightlifting "clean" where you can use your legs too, and then move it to your back (see
www.exrx.net for an example of upright row vs. clean movements) . And try to duck under the back rather than lift it over your head (if you can do this safely).
2) you could switch from back squats to front squats (again, exrx has pictures)
3) ultimately, as you add weight, you'll need to take the weight off a squat rack where you duck under the bar instead of trying to lift it up.
How much weight total are you using for your heavy sets of squats? This could allow us to suggest workarounds for squat rack if we know how much weight is being discussed?
DL - remember your arms are just straight hooks that connect you to the bar, and your back is just a continuation to connect to your hips. Don't let your shoulders or your back round or attempt to do any of the work - it should almost be as if a Barbie or Ken Doll is doing this (from the hips up
your knees can/do bend of course).
are you doing regular squat down and pick it up deadlifts or are you doing SLDL/Romanian DL/keystone DL? if the latter, try to imagine the Ken doll doing the motion - no back movement, just hips/glutes/hamstrings and possibly knees are bending and straightening.