Most likely you have the shoe adjustment way too loose.
After you restring the cable, put the drum and wheel on, from the inside tighten the adjuster till it drags. Then have someone LIGHTLY step on the brake pedal to center the shoe assembly. It won't drag anymore.
Again, tighten till it drags, then step on the brake pedal to center it.
Keep doing that until the wheel will not turn - after the pedal has been applied and released.
Now, poke a small screwdriver in through the slot and push the self adjuster arm away from the star wheel - GENTLY! (Toward the outside of the vehicle.)
Use a brake spoon to turn the star wheel DOWN a few clicks while holding the adjuster away - 6 or 8 clicks.
Step on the pedal again, repeat if needed.
Once it stops dragging, or just barely drags, you are done.
Most people when they adjust brakes they don't keep stepping on the pedal to center the shoes, and end up way too loose.
Centering is very important.