Sugiyama Doesn't Minimize Crossings

[MNandor]

What I'm looking to achieve is minimize the amount of lines crossing each other. I find them visually displeasing. I understand that some crossings are necessary, but sometimes I see crossings that could have been avoided.

The repo itself has an example

This is what's shown:

This is what I'd like to see:

My artistic skills clearly are limited, but I hope to show that by moving the line that I've redrawn in blue, we can reduce crossings.

I know the problem is NP-hard, but I wonder if there are improvements that could be made.