alt Hacker News> Circuit extraction can be done with magic.
So that was the missing part for me! I did it from scratch (with custom Python script with gdstk and shapely) (the GDS file does have the cells annotated, so not a big problem but still). I was thinking about scripting the "trace net" tool in klayout but decided that's going to probably bring its own can of worms...
You can give the cell instances a stable name by setting GDS property 98, which I learned about from my reconnaissance of the puzzle author's github and sky130 visualization tool. This way I was able to spot check a pass over the netlist that broke up the regions into a hierarchical design.
I'd like to do a full writeup but haven't had the time.