Thanks guys.
I've been to the Westin before and have taken the train. As I'm only going to be on the ground for 36 hours or so, I'll not have any more than an overnight bag and a briefcase.
Basically, it seems that I should take the first N'EX I can get and just get off at whichever of these stops it goes to. I know I need a ticket to the correct destination, but I can ask at the counter.