Rear Brakes lock up

I have a 88 civic lx in which the rear brakes lock up. from what I can tell it looks like it is being caused by the backing plate. I have not been able to find new backing plates and most likely will have to put used ones on. I don't know if I can convert over to disc brakes if I cant find used backing plates. any and all suggestions are welcome.
the parking brake works fine. when driving you can hear the pads rub on the drum and after inspection you can see wear on the sides of the pads.

I replaced them about 5000 miles ago the 1st time they locked up and had to install washers on the studs as the pads where dragging against the backing plate. this helped but I thing that the backing plate is breaking down and starting to fail. I will try adjusting them again.