Hi eric, I've attached here a layout with your curves that will now work for Network. The difference is that I cut the ellipse up into 2 pieces.
The reason why that works is that now there are 3 long pieces here:
and now those 3 long lines work the same as lines of longitude on a globe, and can be mapped to a 2D grid pattern. Network has to be able to map the curves into a flat 2D grid like that in order to work.
Here are a few previous threads discussing similar network layout stuff: