Hello there. I see you had an earlier discussion with Emily about these items. As Emily said, there are no spiral balances that are 1/2" in diameter. They will either be 3/8" or 5/8". It's best to remove the old spiral balance from the window to obtain an accurate reading. If it's 3/8", you'll need a Series 900. If it's 5/8" (or 9/16"), go with the Series 600.
You then have to choose a length for the spiral balance. Measure that metal tube, up to but not including the colored tip, to determine this. Finally, you have to choose a color tip option, which denotes the strength of the balance. Your old balance's tip is a faded white that is from an outmoded rating system. Weigh the window sash these spiral balances support. You can then use that exact weight to choose the correct color tip option.
As far as the pivot shoe, we have none like that that our 1/4" thick. Please double-check this dimension. Be precise as possible. Also confirm it is 1-1/4" wide.
See the videos I've listed on this page for further removal and replacement guidance. Let me know if you have questions.