Tracking down pull to left under braking...

[Project1970]

I've been tracking down a pull to the left under braking for a while now. I'm 95% certain it's the rear brakes that have been causing this, since the first set of shoes I pulled off were badly worn on the left but only partially worn on the right, and the set I took in today was cracked (overheated) on the left but not the right. Today, I replaced the parking brake cables, since the return springs on both were kinda toasted, especially the driver's side...but it's still got a bit of a pull to the left. Less, but still there.

The backing plate on the driver's side has some grooving on the 6 points where the shoes rub against it; is it possible that this odd wear (not present on the right side) is causing the driver's side to hang up to an extent? And if so...how hard is it to replace the backing plate?

12-bolt rear on my '70, by the way...