And that twisting was what drove me to always do bias binding. EVERY time I tried binding that wasn't bias I had a mess.
I don't iron my binding in half. That creates more problems for me. I just fold it in half and slightly stretch the binding as I sew it to the quilt. And I mean, very slightly. The feed dogs will almost always pull a little bit more bottom material through and the top (which is binding in this case) will be a tiny bit slack. This caused a problem for me. So lightly stretching the top keeps everything even. I only pin on the corners. I either pool the binding in my lap or over my right shoulder. Both ways work well for me. Rolling the binding on something just meant I ended up with it rolling away from me.