I had a chat with the Chevy parts guy this morning. The part I ordered is exactly the part I have, so my problem is not an incorrect parking brake lever. In the photo below, I have the brake bar installed. You can see how the shoes are held apart at the top. My parking brake pedal is in the full up position. What you can't see in this photo is that the top of the right-hand shoe is not touching the backing plate. The parking brake lever is bearing against the raised central portion of the backing plate, which prevents the shoe from resting against the backing plate. My theory is that the lever is supposed to be more to the right, where it would not bear against the raised central portion of the backing plate. That would allow the top of the shoe to rest against the backing plate, and it would reduce the separation between the tops of the shoes.

The parts guy had an excellent drawing of my brakes, far better than what's in the Service Manual. It bothers me that GM has this excellent VIN-based parts information on-line, but they deny their customers access. So we go buy Chilton's manuals and Service Manuals etc., and we get generic info that is not at all specific to our vehicles. All the while GM's online systems have everything we need, but they deny us access. Grumble.
One thought would be to find the adjustment for the length of the cable and loosen it, but I find no such adjustment. This photo shows where the cable starts at the brake pedal.
This shows the equalizer, with an adjustment for the right-hand parking brake. I haven't even touched the brakes on the right side yet. You can see a bit of the black cable housing leading to the left rear brake.
Here you can see the rest of that black cable housing, leading to the left rear brake.
No adjustment.
What should I do next?
The parts guy gave me the part info for these cables, including the lengths. I could take out the cables and measure them. New cables are $25, $50 and $70 respectively for front, rear right, and rear left. Maybe I should just hold my nose and order a full set. Or perhaps you folks can point me to a way to adjust the length of the cables?
Thanks,
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