Photos attached of my leg training ideology.
Since you mentioned leg press first, if you can squat (front and back), hack squat, and hex bar deadlift add those in ASAP.
As far as bringing up the sweep. Narrow your stance on everything; I don’t care what anyone says it works. Get DEEP in squats with tons of knee flexion instead of sitting your ass back (IE drop straight down). Add in some extensions with your toes pointed slightly in. Pin your quads out there (for feeling). Lunges with a close step and lots of knee flexion (drop down, don’t move forward over the knee or it’ll be glutes).
Do realize that the overall shape and proportion your legs take is highly genetic. The 4 heads tie in where they tie in and there’s no changing it.