Raptor,
What you are talking about with the function of the hamstrings is more of an issue in regards to the prevention of ACL tears (supposedly, the jury is still out exactly how much that function helps). The role of the hamstring when the leg is bent slightly is to prevent forward translation/movement of the top of the tibia on the femur.
If your knee is giving out on jumps, I believe this is purely the function of the quad muscle group, although how is your ankle stiffness? If you are a hard heel planter that maybe could make things a little harder for your other muscle groups.
The hamstring really only does 2 things in dynamic movement, flexes the knee and extends the hip. The hip extension segment is the part of one leg jumping that you should care about and it happens after the whole "knee buckle phase" has passed.
Also, your quads can be strong, but can they fire quickly? I do see you do a few single leg drops, but from a very low box, maybe you should try a higher box and put the pressure on the front 2/3 of your foot.
I feel I am correct in this post, but maybe there is research out there I have not seen to prove me wrong