It sounds to me like your rear brake is "touchy". If that's the case, buy new wheel cylinders... assuming everything else is correct. When wheel cylinders start to fail they can become very touchy and lock up easily. Even though it only sounds like one is failing, replace them as pairs to save yourself headache later.
By wheel cylinders do you mean the brake cylinders on the rear drums themselves?
Also, everytime you back up the adjuster is supposed to get one notch tighter. I never had any problems with that, but maybe you spend un unusual amount of time backing up?
I don't know if it is possible to install the adjuster backwards... . or shoes for that matter if the adjuster was left in place? I have never seen inside a dodge brake drum so I cannot say for sure, but the last truck I had (94 Chevy) made it impossible to install parts backwards. (install holes for adjuster assembly were only on one shoe, etc. ) The problem with my Chebby was the axle seals. The were prone to go out and leak lube into the drum. This caused considerable grabbing and locking up as well. I have no idea what condition your drums are in, just a thought.
I will probably goe ahead and replace the wheel cylinders, just replaced rotors/pads/bearings/drums/shoes about 3 months ago, pretty sure there are no leaks in the rearend. But about 2 months ago my uncle and I left here (Calera south of Birmingham)on a fri evening pulling a 28' enclosed trailer and drove straight to Hartford Ct. non stop loaded up a 29 Ford Model A Woody Station wagon, stayed about 2 hours and came straight back, got home about 10am on Sunday (2400 miles). On one leg of the trip the parking brake was left slightly on for who knows how long, my uncle was driving at the time and got everything very hot. The ABS and brake light were always on because an issue with the rear sensor so he did not realize the brake was on. Could be a cause for what issues I have. By the way here is a pic of the Woody View attachment 71057