I was obscenely overweight as a child, to the point of having a "beer belly," (42in. waistline at 8) so it was like wearing a weighted vest all-the-time. I also did an absolute ton of martial arts though (old-school stuff to boot). With all the deep squats-which were held for over 20 minutes before movement was allowed- and my being slightly bigger (taller+wider) than just about everybody else in class, Sensei made it a point for me to do a "SIDE-KICKS!" for an hour a day, every day, against a 100lb punching bag that was swung at me, then for an hour of sparring where the foot reigned supreme. Thusly, I have really developed calves and thighs.
As for one of the "squats" in question, put your heels together with both feet pointed 45 degrees outward; take a 1-2 foot step (of equal length) with both legs, squat down until you are able to place your hands on your knees while keeping your back straight and your knees pushed out. Proceed to hold this stance for the next 20 minutes and have random people push straight down on your shoulders to make it harder. After a quick stretch, repeat this for the next hour and only stop to do exhaustive bursts of cardio.
Your spine (and butt) should be directly above the corner made if a straight line were to be draw through the middle of both feet. Imagine the lines made when two walls meet a floor.
My advice to you is this:
1. Don't fear the treadmill. Set it at MAX incline and walk for about an hour-and-a-half on it at around 2.5-3.2mph for the entire time you are on said treadmill. However, a slight jog at a lesser incline to get the blood flowing beforehand is never a bad thing.
2. Possibly take up some form of martial art (taekwondo included).
3. Wear a weighted vest under your clothes all day long.
4. If it is safe, walk on the balls of your feet when going up stairs. You can also just push up on the balls of your feet when waiting in any standing/seated situation.
5. After following step 1., do various things in your gym-leg press included, once legs have recovered... enough; lather, rinse, and repeat. If your calves start cramping, or feel as though they might, get off the treadmill immediately and go sit on one of the bikes that requires the leg press posture. Make sure you stretch deep after doing this.
hope you found at least part of this helpful, best of luck.