Window balance
I also have 31HD that measures 31 15/16 x 9/16 x 1/2.
the windows are double channeling and the places I've researched have said they are no longer avail.
Hello,
Your channel balance resembles the S770. With that being said, I'd recommend double checking your balance lengths since the stamp codes should either match the length or the length should be 1" mort. The 27HD is 1" less than the 28" length you provided, where the 31HD stamp of your other balance would be 32" long if it follows the same pattern.
For the 28" balances, see the S770-28 (28C) calibrated to support a sash between 18-23 pounds.
You'll also need to weigh the sash supported by the longer balances to determine which option you'll need. There is a chart on the balance product pages that explains how to choose your option based on the sash weight.
As for the pivot shoe, take a look at the 15-121. This is 1-1/4" wide and 9/16" thick as shown below. It looks like it has the same center cam as yours, too, so I think it can connect to the pivot bar. You can double-check to be sure: the cam slot on this shoe is 5/16" wide and 3/16" high. It's made to work with pivot bars like our 26-040.
Note that this style pivot shoe is made for spiral balances, but I still think it can still work for your channel balances if it matches the specifications of your original shoe. After all, you only need to pinch the cord between the slots in the metal bracket and "anchor" the clip underneath them. If your old pivot shoes have been working fine in that capacity all these years, then you should be good to go.