In college during one spring break I unintentionally went on a 27-hour cycle and rotated through an entire week, 3 hours per day. And that's with actual sunlight still in the sky to theoretically keep me in line. I was pretty happy being up 17 hours and sleeping 10 (or 18/9) without much trouble, other than not always having a way to get something to eat when I was hungry.
An extra 40 minutes sounds relatively minor, especially if the whole world is on the same schedule. I'd say wake 20/sleep 20, or, if it's really that exhausting, just sleep the extra 40.