SusieQOH

Hey everyone,
I made this pattern from Bev McCullough of Flamingotoes.

Here's my question:
How in the world do you get the other side of the binding to look better? I have such a hard time with this. I usually hand sew the back of the binding but I wanted to get this one done quickly. No matter how carefully I sew, the back side never looks good. The last picture shows what I mean.
Any help is appreciated!