Spiral balance 31" x 5/8" white tip

Thanks for writing in. I agree, if your balance's outer tube is 31" long and 5/8" in diameter, then the S600-31 Tilt Window Spiral Balance should work for you. White tips are from older rating systems and therefore unreliable, but as you say, if the window sash weighs exactly 28 lbs, the blue tip option should be correct for you. 

To replace the pivot shoe in an aluminum window there should be a metal stop screw on the top of the window sash. This screw holds the stop and balance. After you remove the stop and balance, there should be a cut out so you can remove and install the pivot shoe. If there is none, you can make a cutout yourself. See the video below.