Replaced the part.
The most challenging part of the repair was finding the model number on my washing machine. Once I found that, it was simple to track down the part I needed and replace the board.
Of the 10 or so cables, one cable was not able to fit all of the way onto the board. It seems like the plastic fitting was a few millimeters off. It fit well enough to form a circuit. It seems possible that I will need to reset that cable down the road if an unbalanced load occurs.