Q:

Time for morning prayer when flying over Greenland and seeing the sun rise twice

Last year I flew from Tel Aviv to Los Angeles. The flight leaves at night (1am) and, in the winter, lands when it is still night (630am). However during the flight, over Greenland, one sees the sun then it disappears somewhere over Canada and it is night again until the "real sunrise" on the West Coast.
In this case, when is the right time for shaharit?
Normally one prays at the time of one's current location. But in this case the sun over Greenland is not the "real morning" for that day. Or maybe there are two mornings?
This is important because if the time for prayer is over Greenland and one doesn't pray there - then one cannot eat during the next 8-9 hours until one prays on the West Coast.
And if the time for prayer is over the West Coast then one cannot pray over Greenland.
I could not find answers for this situation. Has anyone encountered this situation and asked a rav? Or do you have sources that would explicity address this?
PS. See here for the return question on not praying arvit if the sun never sets

A:

From http://ravbaruch.com/AskTheRabbi.asp?QID=92#_ftn2:

Reportedly, Rav S. Z. Auerbach z’’l and Rav Moshe Feinstein z’’l ruled that if one experiences two sunrises on the same day of the week, one is obligated in only one tefilloh. The time cycle for tefilloh is once a day, regardless of how many nightfall’s and sunrises there are on that day. Since they hold that tefilloh is day-sensitive and not sunrise-sunset–sensitive, it follows that someone who davens and then crosses the dateline westward (leading into the following day) has to daven again even though he did not experience a sunset or second sunrise. If it is the day that requires the tefilloh, then since he is now in a new day, he must fulfill that day’s tefilloh obligation.
Rav Elyashiv is reported to hold the opposite opinion and to consider
  tefilloh to be sunrise-sunset–sensitive. In that case, two sunrises in
  one day obligate the person in two tefillos, whereas crossing the
  dateline in a westward direction (effectively stepping into the next
  day without nightfall) does not require a new tefilloh. These two
  views regarding tefilloh are expounded upon in Rav Betzalel Stern’s
  Betzel Hachochmo, and Rav Yechezkel Roth’s Emek Hateshuva.

