Yes, in my case Hamstring strength has cured my buttwink and gotten me to the point where I don’t think depth - I just drop down and rebound up. You need to find a position where your body is locked in and you can’t go deeper. Then you just hit position withour thinking.
Currently, I treat the Hips, Adductors, and Hamstrings as primary movers (in extension). I train conjugate and after the ME or DE movement I use one heavy hip hinging movement (RDL, GM, SDL, etc.) and then a leg curl variation. This way the hamstring is worked in bothe directions since it spans two joints.
I also do calf work because as Ed Coan mentioned the calf functions to stabilize the lower leg while pulling the shin backwards. I learned this somewhat by accident. A year ago I partially tore the inner part of my right Gastroc and after rehab, when squatting I initially had problems stabilizing the walkout and also my right leg would shift forward and cause a rotation in the bottom of the squat.
As for knee stability it is a combination of knee isolation (leg extensions, leg curl and adductor/abductor work). Hamstrings should be about 2/3 as strong as quads. Right now my leg curls are still lagging (about 55%) with respect to quad strength. The Ham work has also improved deadlift poundage and mechanics.
Also, don’t accept popular wisdom. I have always found that the “worthless adductor/abductor” machines have always helped when included as prehab work for sets of 25-30 reps. There is no such thing asa bad exercise, only inappropriate programming.
Finally, you should really look into westside programming.It demands a fair amount of study but the beauty of the program is that it is infinitely customizeable. My only caution is that you have a long enough training history so that technique is dialed in and you can analyze whta your body is doing.