Pivot shoe for 31B BSI balance?

A home owner from Warren, MI says:

I need to replace the shoes in one on my windows.
The channel balance stamp is 31B BSI.
I ordered some parts from you (15-194 : 1" T-Lock Balance Shoe) but it didn't fit. Can you help me?
A user submitted image of window balance shoe
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Paul from SWISCO responded:
Thanks for posting! Please take a look at our 15-169 Snap-Lock pivot shoe and compare it to your own hardware. Do you think this might work? Be sure to compare the width and thickness. If you aren't sure, can you please give me the dimensions of your current shoe?
A quick learner from Warren, MI says:
I did consider 15-169; however, the width is 1.25" and the thickness is 0.5". My part is less than 1" width (0.9") and it seems to be 3/8" thick except where the metal piece is about 1/5". The height is just larger than 1.0"

I was lookinf at the 15-109. The dimension looks about right...but I don't know if it is going to fit. The part I ordered before was 0.5" thick and it made a bulge on the track. The width was fine.
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Paul from SWISCO responded:
I see. In that case, can we see what your balance looks like? Please make sure to take a picture of how the balance attaches to the shoe. That would help us determine what would be best for you.
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