Having a fit with the passenger's drum on '67 Dart

The adjuster is completely tightened down, and the back brakes only have the strut bar and spring. That's what the shop manual shows, too, that the bar and spring only go on the back.

You are confusing the brake shoe adjuster (star wheel) with the parking brake cable adjustment nut on the long parking brake cable. Loosen up the adjuster nut on the rear cable. I'm still pretty sure that you are missing the parking brake strut bar and spring on the rear if the pic you are showing is the rear. They are an integral part of the parking brake.
Here is the procedure for your rear brakes:

1. Release parking brake lever and loosen cable adjusting nut to be sure cable is slack.
2. With rear wheel brakes properly adjusted (star wheel), tighten cable adjusting nut until a slight drag is felt when the rear wheels are rotated. Then loosen the cable adjusting nut until both rear wheels can be rotated freely.
3. To complete the operation, back off an additional two turns of the cable adjusting nut.
4. Apply and release parking brake several times to be sure rear wheels are not dragging wen cable is in released position.