Measurement
Thanks for posting! I am confident that we can offer a replacement balance for the one you have pictured here, however, I'll need to see a clearer photo of both the top and bottom attachments. It would help to see the photos from a "front" profile view, on the side where the spring is exposed.
Thanks for the photos. It appears you have the S350-29 channel balance with a 2830 stamp. These balances are assembled with a 19-002 non-winged top guide and a winged 15-004 (1-3/32" deep) bottom shoe.
It is likely that the 1-3/32" measurement is the one you'll need. Using a measuring tape might give you a more accurate measurement.
It is likely that the measurement is 1-3/32". In our experience, there hasn't been a shoe made with a 1-1/4" measurement. So the Series 350 balance recommended would be what you need as a replacement.
As mentioned, it has the non-winged top and winged bottom, like your balances.