Use an EK credit card if you have one. Not sure how long those would take to post though.
I'd say take a quick flight on United or Continental, but it doesn't sound like you have time for that. Hotels, car rentals etc could work. Take a look at the earning miles section on the website and see if anything there is viable.
And make sure there is upgrade availability!
Edited to add: And the flight back is longer, so maybe you want to save the miles for the way back. Then you would have enough from your outbound trip.