I do not have the experience that most of these guys have, but I do train for powerlifting and I plan to compete after I am done playing rugby. Which will be this spring sometime.
I do pretty wide stance squats, I feel a lot stronger wide, and for me it is easier to get out of the hole. I do not know if this is just because this is how I train squats or it is my body. Box squats have been the key to my lifting success. They taught how far down I have to go to hit parallel and also really helped my hip strength.
I recently became obsessed with jump stretch bands, and I think that the speed days for both bench and squat have significantly helped all my lifts and taught me how to explode out of the bottom. As far as pausing at the bottom I would not worry about that too much, and just focus on upping your weight in the bench and pounding your triceps. If you have not done a lot of board presses you will probably love them, because you can put some extra weight on.