I know it's pushing it, but couldn't one go w/ 1 team of 5 (probably 6 for minimal downtime/buffer?) in NA to cover 24/7?
When I was growing up, there was a 24/7 coal-mine near-by and everyone was on two-week rotations for their shift. Which (naturally) sucked. Eternal jet-lag. I thought that letting people simple pick their preferred, and stick to it would solve the suckiness...