I love your maps!
Yes, I tried to bend and squish the lines, but as you can imagine, the scale is so exaggerated at the poles that narrowing the lines by just a few pixels made huge changes. And curves...you think just altering the start and stop points will adjust the curve correctly but the middle of the curve has to be changed too, and it's not a smooth curve. To get an adjusted arc, you have to draw a line that changes width and angle along the way. Finally, I just gave up and settled for them meeting at the right place, albeit in converging, narrowing lines. The software program I used has several mapping modes. One of them, the spherical one, did a fairly good job of making the lines curved, but that was after a ton of fiddling that I couldn't reproduce again. Plus, the lines were fat and the continents got really fat at the equator.
I think we will persevere though. I think part of the fun is remembering it's an ongoing work.