36" Channel Balance Markings appear to be 3530 then a small upper case E followed by BS in a larger font.

Hi Brandi, thanks for the thorough information. That stamp code actually just tells us the strength of the balance (and the 3530 is the only pertinent part, in this case), not its identity. For the identity, we go by the nylon attachments. It looks like you have either an S380-36 or S385-26. The only difference between these two channel balances is the depth of the bottom nylon shoe, or the measurement from 'heel' to 'toe'. See the diagram below for reference. Compare both balances with your old hardware to see what matches best. Based on your photos, it looks like that measurement is 1", and therefore you'd want the S380-36; but double check to be certain. In either case, for a stamp option, choose 3530. Let me know if you have any questions about any of this! 

Comparison of the S380 and S385 balance shoes.