The problem you are describing is that the cable is getting stuck somewhere. When you disengage the left rear wheel cable, the other wheel cable or the center cable will take up the slack. With drum brakes, the wheels get adjusted when the wheels are in reverse, once the brakes are applied, the adjuster advances 1 tooth. The cable on the other hand will push the lever forward forcing the brake shoes to advance. On some drum systems the adjuster is actuated by the cables, so if the cable isn't used at least once a week the cable seizes on. In your case, the parking lever is most likely still too far out preventing the adjuster to do it's job.
Note: The drums are scored from the heat so you will have to sand them with emery cloth.
post back your findings.