You’re performing your DL like a first pull of a clean.
Watch Bolton’s 971 DL at the end of this video…
A big DL takes advantage of the hip drive to move his shoulders behind the bar and shift the weight onto the heels. I routinely have to stop myself from falling backwards on light warm-up sets because I force my toes up with my weight on my heels.
Obviously your toes are going to be in contact with the ground on a heavier DL, but the principle is the same.
Also, when you drive under don’t be afraid to drive your shins into the bar, if your knee angle is over 90 degrees you’ll have no problems clearing the knees without having to shift your weight foreword.
Your squat problem is actually not a different problem.
The first thing you do is drift foreword onto your toes.
You’re torso quickly follows by flattening out into an impossible recovery position.
For the squats I would do work sets at 225 x 3 with 5 lb plates under your heels. Concentrating on getting your toes up on the concentric(they may not actually come off the ground).
For DL I would do cluster sets with 135, 225, 315 concentrating on driving under and through the heels(toes up). Take 5-10 sec rest in between and set up new every time to really learn the driving position. Once you feel comfortable with your weight on your heels you can do work sets of 315 x 3 or continue to do cluster sets working up to 365 and beyond.
Also, if your’e going to dip and rip, be aware that the drive under is what’s going to generate that large elastic and myotatic reflex and you’ve only got one chance to get it right with that style of descent.