I'm confused. Is Las Vegas your destination? Where are you flying from? When did you get your Amex Platinum card?
If Las Vegas is your destination, what do you think is going to be so great about the Centurion Lounge. I've been to the one in Miami and while it is nice, it's not a destination. Don't let the travel bloggers try to convince you that it's just as nice as a fancy spa or bar.
I would pick up your bags when you land and go to your destination.