I used choice air and booked a nonstop to London with transfers. It worked out that the combo was less than just the flight alone had I booked it on my own. And it was a fully refundable flight. Lots of other folks had stops and they were totally exhausted.
It was pretty nice to see a Royal Caribbean rep at the airport waiting for us.
And Dave, I highly recommend virgin Atlantic. They wined and dined us the whole way!