Well, I think 160s are a bit short for someone 6'2", 245, first. I'm 6'5", 225 and my skis are 195s. I don't recommend that you jump to 195s (I've been skiing a long time) but don't think 160s will give you enough ski. Try 170 - 180.
But I think this is more a matter of learning to be comfortable with speed and developing technique. You are probably feeling that burn on the tops of your thighs. That's a build up of lactic acid in your muscles, and it basically comes from muscle tension. The muscles in your leg are tensed up and expending energy far in excess of what you need to control your speed.
Once you become comfortable with your ability to stop in a short distance from any speed (and you will), you will find that you are more relaxed and you will feel a lot less of that burn, or none at all.
A couple of things to think about.
If you are mostly skiing on packed, groomed runs, longer skis will help a lot - then keep the weight on the front end (tips) of the skis. This is a little counter intuitive (you basically are leaning forward while going down a hill) but you will find that you have much better control.
If you are in wet, heavy, ungroomed snow or powder, you will want to keep your weight more balanced, front to back, or even put your weight more on the back end (tails) of the skis.