i have the same kind of issue. i do some squat morning on the heavier squats, lol. a trainer friend that was on a seminar tour stopped by town and we worked out together. he has experience in powerlifting as his gym hosts 2 APA events a year and he competes at times.
he was telling me about glue ham raises so i gave some a try. couldnt do one without help. i can do a crap ton with goodmorning and stiff legged deads. and yes, crap ton is a scientifically measured amount.
he informed me that i probably have the strength, they are just lazy. and well, making them stronger will help keep your back straight. i was also doing mostly high bar narrow stance squats till recently. so moving to a low bar with side stance my back side is too weak in comparison. so i whipped up a poor mans glute ham device and got some bands for assistance to help work that back side and get it working harder. as well as the advice i threw up already.
im looking forward to what he calls squatters ass. looking like i have a kardashian ass, lol.