The problem became obvious when I attempted to install the new leading shoes, so at that point the adjuster and springs were not yet installed.
The cable moves freely from front to back and to both wheels, with no sign of corrosion on them.
The diagram you referred me to indicates that the tension equalizer is applicable to the 2004 Cavalier, but when the corresponding part number is searched on the GM Parts website it comes up as applicable only to the Olds Aurora.
At any rate, having run out of time for this project, I left the brake lever detached on the one side, without much worry since the it's an automatic. Also, according to what I've read the self-adjusting system on these later models doesn't require actuation of the brake lever.
I thank you for the suggestions and the prompt responses.