I don't know if I really understand where the binding "twisted" on the quilt.
Regardless, the best advice I can give you is to watch these videos by Sharon Schamber :
http://www.youtube.com/watch?v=4PE0Yq9iGlc
There are 3 parts.
She's really thought through each and every issue.
Even if decide not to follow all of her steps, at least you'll understand why she does it the way she does, and what problems she's preventing and avoiding with her methods.
I'm positive you will find the answer to your problem somewhere in there. ;-)
And yes to starch. Always, always a big yes to starch. And more starch.