I always confuse Westin and Sheraton! Sorry about that.
With a later departure is chance the shuttle, but with a 740 am international departure I sure don't want to be late.
I've done 7:40 from the Hyatt. But with carry on bags only.
If you really want to be sure and really don't want to miss the flight, just pay the money and stay at the Sheraton. It's expensive, but worth it in cases like this.