When learning to play you are always told to sit straight up and on the edge of your chair. When you stand that is just not totally possible. Ever notice when you see jazz musicians play that kinda hunch over? Try bending over a little more and higher the strap. Just work at it and you'll eventually find something comfortable.
Have you ever considered to go to a shop where they repair saxes. It is possible, that for you the balance of the instrument is not accurately. This can happen if you’re too long or short, or like me very big.
Then they can braze an new ring on your sax so you can play standing up. Some players like Clarence Clemons have two points on their sax and they hang it over their back like a guitar belt. This also helps to prevent neck problems .