How to assemble '70s-era center-pull brake
I finally got it to work by employing a third "hand" as such:


Disassemble both arms.
Start with the innermost arm, squeezing the arm into place so that, when it is in its "resting" position, the spring lies inside the two respective hooks on the inner plate and the arm itself.
Screw the retaining bolt for the inner arm all the way, so that the arm remains on the bike without falling off.
Grab the second (outermost) arm.
Put the retaining bolt into the arm and then push it just barely through so that you have enough space to put the washer on the other side, and do so.
Adhere the bolt to the arm temporarily by covering the head of the washer in adhesive tape and then wrapping it around the arm so that it holds the bolt in place by itself. Cut a ring in the tape inside the washer so that the bolt can be screwed in easily.
Squeeze the second arm into place in a similar fashion to that used for the first arm and hold it in that position with your hand.
In order to keep the spring from "jumping" out of place, push the retaining bolt through the washer and into the retaining plate. Hold the entire assembly together by pushing on the head of the bolt with your thumb.
With your thumb on the bolt, it is now possible to release your hand grip on the arm itself and then to use the hand to properly position the bolt into the plate and then screw the bolt securely into the plate.