After having gotten over the hilarity of yesterday evening's discovery, I took a little bit of a closer look at my results. Obviously, the result is entirely hinging on aspects of the implementation, not least that the starting configuration was drawn by hand so it's unbalanced.
The *really* interesting observation is what's happened to Tiphereth (labelled as 5 in the diagram below). It has gone from the most central position to having flipped outside of the configuration meaning that the central pillar runs mostly up the left hand side. You can see that this would have happened because all the forces are exerted by the paths, and I set all of their resting lengths and restitution coefficients to be equal (the best example of this being 8-9, which will be at the target length due to no competing forces). Because Tiphereth has most links, the lowest energy configuration is if it flips to the outside.
We're going to call this phenomenon "Tiphereth Inversion"