Old BSI part number does not match current convetions

A home owner from Seattle says:
This balance is from a 1984-1985 era window. I need a replacement as one of spring's end hooks broke. It is clearly stamped with "B.S.I." and has "12 A" on it. I cannot find "A" as part of a numbering scheme.

The metal channel length is 13".
The window weighs 5lb 6oz.
Included pictures show the end nylon pieces from a couple of angles.

What part number(s) should I be trying to acquire? I think I should replace both balances while I am at it.Thank you!
Thumbnail of the uploaded file named Channel Balance Assembly
Thumbnail of the uploaded file named Balance Wingless Top Guide
Thumbnail of the uploaded file named Wingless Top Guide
Thumbnail of the uploaded file named Channel Balance Shoe
Thumbnail of the uploaded file named 12 A Balance Stamp
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Jasmine from SWISCO responded:

Thanks for posting! Your channel balances appear to be either the S351-13 with a 1" shoe or the S390-13 with a 1-1/8" shoe. To determine which series is needed for your window, look over the dimensions from the diagram below to confirm the depth of your bottom shoe. 

You should be able to use the 1210 stamp option, which can support a sash weighing 3 to 6lbs.

Comparison of the S351 and S390 balance shoes.
Comparison of the S351 and S390 balance shoes.

A home owner from Seattle says:
Thank you for your reply!
I've measured the shoe and it appears to be a little more than halfway between 1" and 1-1/8" inches. Measured out to 1-5/64 inches. I'm assuming I should opt for the larger series S390?
Thumbnail of the uploaded file named IMG_1290.jpeg
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Jasmine from SWISCO responded:

I'm happy to help! Since the shoe is over 1", I do believe the S390-13 is the correct replacement.

Please let me know if there is anything else I can assist with.

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