Hello there!
Thank you for reaching out to us. I'm not sure if we'll be able to help with this. To help confirm, can you tell us if this balance installs at the top of the track with a screw or a hook?
That part is the pivot bar but what we're asking for is at the top of the window track. There should be a balance pulley cord with a screw tab or hook attached at the end of it. May we see a photo of that? Removing the balance may be necessary.
Thank you! Since the hole is squared-shaped, you could consider the S795-26 and 26-200 screw plug. The video below will go over the details. We can't promise it will work but it is the best option we can offer. Note that the 15-272 shoe won't fit in our metal channel but we hope that the S795 t-lock shoe can work as is.
Please let us know if you decide to try this out! We'd be interested in knowing how the repair goes.