In fact I was misunderstanding the schema. skoormit was able to supply the insight I needed to make this much nicer graph:
It turns out that the database classifies techs into Categories, Fields, and Types, all at the same time. I suspect that this has evolved over Aurora's lifetime; the result is a bit confusing.
I think the next step will be to filter out the unreachable techs used by the spoilers, as well as the secret techs. Then the layout could be better, probably in a lot of ways. All of that can wait for another day, but if anyone has any more ideas please keep posting them.