OK this won't be as good as the triple clamp but better than what you're doing I think. When your string the 7th main on one side hold it on the outside the frame with a starting clamp. This frees up the flying clamp on that side. When you finish the mains on the other side instead of just using one clamp to hold the outside main use both as near together as you can get them. Less twisting that way. After tying off one side repeat on the other.
I have the ability to drive people crazy, not sure if I was born with it or I learned it but I'm damn good at it.