First, there are NO "really good" substitutes.  There are those that you can choke down without gagging (a 3 on a scale of 1-10) and those that the Donner Party would have left untouched (.00000000000000001 on a scale of 1-10).

Moving on to fresh eggs, I have kept them for 5 days or so in some pretty warm temps with no problem.  Keep 'em cool as long as possible by surrounding them with any other refrigerated or frozen items when you pack the food pack.  As long as they stay unbroken you should not have problems.  

It IS possible for eggs to be contaminated with salmonella already when you buy them.  The possibility is extremely remote.  However, that's why eggs are kept refrigerated normally.  I take the eggs and I don't worry about it.  Your chances of getting giardia from swimming in the lake, falling on a portage and breaking an ankle, etc. are much, much greater than the chances that one of your eggs has salmonella inside.  Otherwise they do just fine unrefrigerated for a week or less.  That shell keeps decompositional bacteria out so the egg can't rot.