Just got back from a week and used a one quart wide mouthed Nalgene bottle for egg storage.  On Friday before our trip I cracked 22 large eggs and put them in the bottle without breaking the yolks.  Sunday morning I poured out 10 eggs for breakfast for 5.  Tuesday and Wednesday, 2 eggs each for pancakes.  Thursday, the last 10 were scrambled.  Worked fine.

My food pack has a section of frozen food at the bottom, with 2 quart bottles of ice (my half gallon bottle disappeared.)  It is always in the shade during the day and covered with a double sided reflective insulator.  The frozen stuff is thawed within a few days, but the whole pack stays cool most of the week.  Temps in the low to mid 70's helped.