Pivot shoe

Thanks for posting. I'm afraid it's difficult to say what pivot shoe you need without seeing it removed from the window. The width and thickness of the shoe are also very helpful in determining the right replacement. See the first video below for how to remove your pivot shoe. You will need to remove your channel balance to accomplish this. If your window lacks the cutout that the first video shows, see the second video as well.

My colleague Tom thinks it's the 15-046. This is 1/2" thick rather than 9/16"; but see what you think. The 15-118 is also another possibility, as it seems to cohere to your measurements; but it's difficult to say for sure without having the pivot shoe removed from the window.