I saw that you avoided the problem by reorienting the weave, and noticed that it did follow the edges horizontally.  It looks nice, and kind of makes me think of an outdoor lounge chair.  But I also noticed that you still didn't maintain vertical density, which is what I was talking about.

No, you shouldn't need to do it manually.  I don't see why you should need to manage the vertical shape manually when you already have it following the frame horizontally.  Not that I don't see how your original method caused problems, just that I'd think there would be a fairly similar way to make it work.  Especially since there doesn't seem to be a change in the curve along the x axis.

You might find a generic and holistic solution if you look into chain mail techniques.  Different type of weave, but the same basic issue.  Or, of course, how to make a peacock chair.