OK, it's been five days since I've worked on any of my projects! But it's better to come back late than never.
Tonight, I updated dummy node insertion to use gaps between existing nodes in the layer. However, they don't account for other dummy nodes already there. Also, some normal nodes are colliding as a result of the median ordering step not caring about collisions. So taking care of those two things is the next step before hopefully moving on to edge crossing reduction via swapping.
Despite that stuff missing, this is still an improvement.