Looks like a lot of "experience" out there.
On the electric side, do you have a hard wired ground from each brake back through to the TV? Do not rely on frame ground through the hitch ball.
When breaking in new brakes
, be careful to not let them get too hot. Overheating will cause them to glaze and lose grip.
Drive at a moderate speed - away from traffic.
Apply trailer brakes
hard, then release, a few times with a few minutes between for cooling. This is called burnishing.
It wears off the high spots so the entire surface of shoes makes contact with the drums. Then readjust for proper clearance.
I wonder if somehow you have one with the brake installed backwards. In the forward direction drum brakes
will self energize. In reverse they don't.
Try that weak one in reverse... ???