"Just touching the brake pedal at 20 mph locks up the wheel." I call that grabbing more so than locking. When that happens, it's almost always the self energizing characteristic of drum brakes malfunctioning. One way to know is if it only happens going forward. If it doesn't grab in reverse, it is the a self energizing malfunction. If the anchor pin is mispositioned rearward, or especially if it is low due to a bent backing plate, or a junk chinese repop backing plate, it will cause grabbing. Or if the anchor pin is worn, allowing the top of the front shoe to retract too much. I would try a different backing plate and/or anchor pin. Also, grinding the top of the lining of the front shoe to a bevel could help, but it is a crutch, not fixing the cause. Good luck, Joel