The zipper is in! Woo hoo hoo! (Does victory dance.)
And it was Calliope, whose purse this will eventually be, who pointed me in the right direction. I ended up pinning it in while it was zipped closed and then opening the zipper to sew it in. When I was done, it lined up properly at the corners.
Now all this purse needs is some insides, which I started last night!