If you squated with 625+...raw? (which is near world record class...depending on the bwt) than your legs, hips, glutes,hams and lower back are in almost perfect muscle balance for that lift. No one muscle group is going to dominate over the other, they all work as a balanced unit.. And if those legs don't seem to be responding like you think they should, after handling those huge weights, than you might consider hitting the quads ( I think that may be your main concern) themselves from a different angle.
Might try front squats, which are a prime quad builder. Also BB Hack squats, with the heels resting on a 2" block (or a pair of Olympic plates) ,to shift the focus on the quads section just above the knees (tear drop's). Keep the back straight throughout the lift, no leaning forward until it becomes more like a DL than a squating exercise. Can even use a block under the heels when doing front and regular squats.
A suggestive workout:
Front squats
BB Hack squats
GMornings
or
Leg press..alternate.... one leg at a time.
BB Hack squat
Ham standing leg curl
2 to 3 sets each of 10 - 15 reps. You do not need a lot of endless sets for legs just because their a larger muscle group. Feel free to hit hard the quads & ham's in the same workout. No logical reason to split them up in two different workouts. Approach each leg workout with serious intent. A max effort applied in the shortest period of time. Time the workouts, allowing 90 seconds between each set. And 2 1/2 to 3 minutes between each exercise. Good Luck.