From reading Rabbi Kubers book, Chapter 74 (vol. 3): It seems westward travel over the far north you are in essence going back in time repeating the same day you already had and would not be re-required to daven any tefilos. (This is similar to going eastward over the dateline into yesterday, however by the dateline you are going into yesterday in calender regress while here you are going back in time in clock regress.) So the sunset and sunrise you are watching are actually a rewatching of the ones you saw already. He does say prohibitions will apply like going back into shabbos and the potential for not eating after alos.