With the comments, help on Ravelry and from various e-mail lists and via phone I finally decided how to sew the cloak fabric together. I used a figure 8 stitch while holding the fabric right sides together. Then I flattened the seams and pressed them.

These 2 pictures show how I am sewing the seams.

Here it is partially done. The first seam is finished and I’ve got the second piece pinned in place ready to sew it.

These are the rest of the pieces ready to cut out. I decided to cut the center, then the 2 sides and sew those before cutting the outermost edges.

Here are the 3 middle pieces all finished.