My knees are shot so I always box squat. I wouldn't even consider doing regular squats. At least for me, the pain is from the bottom of the squat that you take away with a box squat.
I don't warm up with lighter squats because even those can cause me knee pain. I do leg extensions because I can make them very light to start, like 70lbs and then work up from there in 20lb increments. And in regards to the number of set on leg presses, I usually do 3 or 4 sets of 20.
Squats bother my knees but machine presses do not. They do strain my lumbar tho Think I will go to your program of lowering the weight and increasing the reps, that should work.