That could work, but it seems like part of the purpose of this form of matrix is to be able to rearrange rows or columns as a unit. (Hence why it says, "Reordering was clearly the most crucial.")

So for example, you might remove all the vertical rods, leave the horizontal ones, and use the horizontal ones to rearrange rows.

This means you'd have to be able to detach the rods from the comb, but that's probably doable. You could build the comb so that the connecting piece clamps onto the end of the rods, for example. Put balls on the ends of the roads and have corresponding voids in the connecting piece and a hinge to close the connecting piece around the balls.