Did you look at any alternative graph layout algorithms? There are non-quadratic ones that are quite good (like Barnes-Hut and its variants). I did a Typescript port of ForceAtlas2 a couple years ago that could run on a Web Worker (so as to not block the interactivity of the graph) but never got around to open sourcing it.

I'd be amazed to see what this level of profiling skill could do on a fancier algorithm.