Coil Balance ID
The pivot shoe looks like our 15-177, which uses our Series 152 Coil Balances. Let me know if you have further questions.
Pivot bars often used with the 15-177 include the 26-446, 26-226, and 26-030. If you can show us one of your originals, preferably undamaged or 'put back together', we can try to determine that for you.
As far as the spring weights, for a 23 lb window, I'd use (1) of the S152-8 8 lb springs and (1) of the S152-4 4 lb springs on both sides of the sash. This would equal 12 lbs of support on either side of the sash, for a total of 24 lbs of support overall. So long as the window weighs exactly 23 lbs, being within 1 lb should be fine.
The 26-226 looks right to me, just double-check the dimensions to confirm.