Well, here’s one working example / proof of concept:
Here I’m using the table of tasks to calculate the X/Y coordinates of each node, then generating SVG for individual nodes and connector lines to parents (as simple as center X/Y of one node to center X/Y of another), and finally combining that all together into something that can be fed to Image(). I had to figure out the algorithm to calculate node position myself (and it’s a pretty naive one, although it gives good-enough results). You can do something similar for your needs. This said, you either need to know how to compose SVG code, or use an editor and then strip out all the bloat that editors usually put inside exported SVG.