As such, I present to you: the Australian Senate Preference Navigator:
It requires a reasonably modern browser (or at least one with SVG support).
No; it's a force-directed graph, meaning that the only metric is how close nodes are to each other, which is calculated from how highly they preference each other. The graph is also draggable, making any sort of left-right alignment impractical.
Since you've mapped the parties to a plane, what do the X and Y dimensions mean? Is there a "left-right" thing?