Well, I sort of have the visualization working. Users can choose which elements to graph (on Firefox) by dragging boxes to move them above or below a plotting line, and they can choose to limit to plotting only one of many options. See below.
On clicking the update chart button, a tree is plotted using the Google Maps API, with branches colored based on whether they have no methods or software, methods but not software, or both methods and software [I originally had it update the map automatically on any change, but this is too slow]. Users can click on nodes to get an info window showing the choices made going from the tree root to the tips and links to any relevant software or methods. Just mousing over a node tells a user what option that node represents (i.e., "Treetype: Unrooted, polytomies, incomplete tree"). If a user has chosen just one setting for an option (as for criterion, below), the edge leading to that node is shorter and light gray edges are shown to indicate the options not examined. See below (click to make larger).
The end product is beautiful and information-rich. It's also VERY slow. It takes literally minutes to generate the plot, and then >10 seconds between clicking on a node and getting the info window. Zooming in or out or moving the plot also take an agonizingly slow time. Getting info from the script that talks to the database to make code for the map takes a while, about 30 seconds, but the real slowdown comes when drawing the map. Google maps are slow with many markers and polylines: the map above has 221 markers and even more polylines, with the three circle polylines having 360 points each (using fewer makes a plot that's too rough). I'll have to decide what to do. I'd stayed away from Processing due to usability concerns, but it seems Google Maps isn't so great, either. I've read a little about generating image tiles rather than markers to speed up the map -- I'll look into this and other options.