50 year old tilt-in window balance mechanism broken

A quick learner from Portland, OR says:

Lifted my window the other day to clean the outside of it and it tilted on an angle and broke one of the plastic "thingies" that the left side of the window attaches to. Couldn't get the "rod" out without breaking the plastic "thingie" even more. 

There is no indication of the manufacturer. On the top of the lower (sliding) window is has instructions for removing the window. On the left it says to lift it 2" and pull in the white tabs (which I didn't follow because the window was surprisingly heavy though I've washed it several time before) and the right side says "TILT LATCH." The plastic piece is 3/4" square with the broken tip sticking out at one corner. Inside the square is a circular piece. 

I was working with a friend who does maintenance for apartments all over the city and had experience with windows like this, but the replacement parts snapped in easily and we had to break the plastic piece whose tip was already broken. thank you for your help!

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Paul from SWISCO responded:

Hello!

Though I can't be certain from these photos, we believe you are showing the old discontinued pivot shoe that has been replaced with the 15-015. The width is 1-1/4" and 17/32" thick but we recommend you remove an undamaged pivot shoe to compare the specifications. We also pulled up media guides on this page regarding the removal of the pivot shoe and the use of the 75-006 charging tool.

A home owner from Portland, OR says:
Thx for your rapid response!

As I said in my first message, I'm working on this with someone who's got a lot more experience than me. I'm hoping he'll take a look at what you wrote and linked to, but I'm thinking that we'll most probably need to buy the tool and get a couple of the pivot shoes. Don't think we can pull the other one out and measure it without a tool. Is that what you'd suggest?
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Paul from SWISCO responded:

Yes, we suggest using the tools mentioned in the video to remove your old pivot shoe. 

A home owner from Portland, OR says:
exactly which tools do I need? Would it best to also get the parts you're assuming we'll need based on my measurements and your experience? Are the parts returnable if they're the wrong one? Seems like we have a chance to save time and shipping fees if we do it this way, yes?
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Paul from SWISCO responded:

You will need a utility knife, snips, the 75-006 charging tool, a flathead screwdriver, and a Phillips-head screwdriver. I believe you have the 15-015 but I still recommend removing an undamaged version to compare and confirm the specifications. You can also return the pivot shoes if they don't pan out. Our return policy can be found here just in case. 

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