Thanks for posting. The Series 600 has an outer tube that is 5/8" in diameter. Now judging from your pictures, your old spiral balances have an outer tube that is less than 1/2" in diameter, closer to 3/8". If so, then you'd need the S900-30 instead. Please compare, and let me know if you have further questions. Also, view our Return Policy here.
Hello again, Jeff! I'm glad to hear our Series 900 worked out for you.
The part you're looking for here is called the pivot shoe. These effectively connect the balance to the sash, while doubling as a kind of hinge mechanism to allow the sash to tilt in for removal and cleaning. Just eyeballing your photos I think you have our 15-045. This seems to match your style pretty closely and is very commonly paired with the Series 900 balance.
I suggest reviewing our dimensions before you buy anything just to be safe. Note that overall height isn't all that important, but width and thickness are paramount. Another important dimension not listed in the below diagram is the size of the cam hole. For this product, that would be 1/4" wide x 3/16" tall. As long as these dimensions match then I am confident it will replace your original.
Lastly, you mentioned advice for installation. I'll share a couple videos that you may find helpful to this end.