verify the pressure is the same is the first step.
prove that then you can dig further, otherwise you are just guessing.
You will have eliminated a lot of questions by doing so and can then move onto the assemblies themselves
Another thought crossed my mind, actually 3:
1. Are you 100 % sure the brake cables between the backing plates and main cable are free and not sticky
2. Possibly try swapping springs side to side. A long shot, but if the one side has weaker springs it will apply sooner.
3. One could try a thin layer of contact cement and thin sandpaper on the inside of the drum. Spay a very light coat of lacquer paint or machinists dye on the shoes, install the drum and see if there is a pattern difference side to side.
I believe you said you swapped the shoes so that would eliminate the friction compound.
Keep us posted
