Your wallhanging is beautiful. Bias binding would have enough give to it to let the hanging lay flat if you feel it needs to.

bias binding has to be used to go around any curves. straight binding is for straight sides. once you cut your bias binding it will bind just fine.

I didnt read the whole thread but I made a set of circles that became a wallhanging quilt. Use a bias binding and then I put the sleeve on with a blind hem stitch. I adjust the stitch so it just barely caught the front of the quilt and used a color in the bobbin that would blend as much as possible.

I did both the binding and the sleeve by machine.

I used one of those "magic" quilt hangers. The slight "bow" in the quilt went toward the back so the edges actually lay flat. It looks very nice. Nice enough to display in my clinic. I would put up a pic but I gave it to my mom after a few years.

bias, carefully place and pin so it doesn't stretch while you are sewing down and then press from top to make it flatter and don't hand sew to tightly. I have done several circular pieces and you just have to go slow and let the binding lay naturally. Am sure some of this has been mentioned above but am in such a rush this morning getting ready to teach at a retreat that I don't have time to read al the advice already given.