Need Pivot Lock Shoes- 1 1/4" wide, 1/2" deep, 2" long

I have a tilted vinyl window in my bathroom that will no longer hold open?..using sticks to prop up. Based on what I've read and viewed on line, it is likely I have broken pivot lock shoes.

What seems confusing from the information I've read is that my channel balance has the spring at the top with the hook into into channel wall and the string system is at the bottom with a hook intended to go into the pivot lock shoe. To add to my frustration, this pivot lock shoe is rectangular so does not pivot, and I'm unable to slide it out at the top of the channel as there is a vinyl panel across the top of the window that I've not been able to remove no matter what I've used to pry or snap off.

So my mission here is to ask your help in identifying a pivot lock shoe part replacement so I can order a few ??..and then get someone local to get the old ones off and the new ones on. If you feel a new channel balance and lock shoe system is a easier/better way to go, I'm agreeable.

Here are pictures of

(1) my pivot lock shoe. It is 1 1/4" wide, 1/2" deep, and 2" long

(2,3,4) channel balance( 16E BS1 TF) - spring and cords seem in good shape

(5) labels from the window?.very likely from the mid 70's. Window is old, but in good shape.

Will really appreciate your help.

Judy

follow-up reply/ information.
Emily
Guess I didn't explain the broken window issue well. The window is shut closed??.it won't stay open at any level. The channel balances are hanging loose in the casings but the pivot lock shoes look broken. I've tested both of the channel balances with a nail on board and the spring and string system works fine. I've tried to reattach the hook on the end of the channel balance to the lock shoes but where they would hook on is broken on both. I'm pretty confident that I need new pivot lock shoes. 1 1/4" wide, 1/2" deep, and 2" long

Emily
Thanks so much for your input! I have ordered the 15-135 's and crossing my fingers I'll be able to open the window after the A/C season is over. I also ordered the big hook Spiral Balance Charging Tool for Non-tilt Windows. That video you provided on how to use with my type of channel balance was very insightful.

Never to old to learn new things!