Sash identification
The Series 350 will not work for you. What you have here is called an extended travel balance, named for its unique configuration, and this can only be supplied as a custom order. No stock balance can replace it.
Before we go any further, can you kindly show me a clearer photo of the hook at the end of the cord? Can you also verify the length of the metal channel? It should be 20-5/8", not 20-11/16". Lastly, how many of these did you need to buy?
If you're measuring 20-5/8" then everything is good to go! That's the size it should be. I'll go ahead and email you a purchase link and price quote that will let you add 10 to your cart. Note that a quantity of 10 qualifies this for a bulk order discount, so the price per balance may go up if you were to order fewer of these in the future.
One last note, for full transparency: the manufacturer discontinued this design and in fact no longer makes it. The good news is that they made an entirely new assembly that will work in all the same applications. I'm telling you this for two reasons: first, the design is a little different (including a slightly longer metal channel). Despite these differences we have tested the balance and can verify that it will replace your original without any alterations needed.
Second, the weight calibration is slightly different. Your old stamp of 2040 is rated to hold a sash weighing 14 through 22 pounds. The new calibration (which is also 2040) is rated to hold 15 through 23 pounds, instead. This is not a huge difference but it IS a difference. Odds are your sash weight falls in the new range without issue, but if I were you I would still weigh your sash just to be 100% sure. I'm happy to set you up with any other weight option you may need, so just let me know and we can reevaluate.