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.

Good question Kingfisher
I also enjoy fresh eggs but have always been too "chicken" (sorry) to bring them along. My alternative, although a compromise has been to boil a dozen eggs and fry a pound of bacon to be eaten cold the first 2 days of the trip. Doing so the first morning out gives you a hot breakfast.  Doing it at home saves you the clean up.
-YB

Powdered eggs generally are not good.  I buy mine at my local food CoOp.  I don't remember the brand but it come in a quart, plastic jar.  That jar lasts me years.  Powdered eggs are great as a substitute for fresh eggs in baking or making a "regular" pancake mix into a "add water only" mix (adding powdered milk as well).

However, I have found one way that powdered eggs are good, and that is as a breakfast burrito.  Here is my recipe:

Breakfast Burrito
     
1/2 cup powdered eggs
Spices (1 teaspoon chili powder blend, 1/4 teaspoon oregano, etc.)
1/4 cup dried beef (or substitute hard salami)
4 teaspoons dried bell peppers
1 Tablespoon dried minced onions
2 teaspoons dried celery
Some hard cheese
2 or 3 Tortillas
     
At Home: Put powdered egg & spices in one bag.  Mix together peppers, onions, and celery in another bag. 

In Camp: Combine the vegetable mixture with 3/4 cups of water and set aside for 15 minutes.  Add powdered egg and meat. Let stand for another 5 minutes.  Fry adding cheese near the end so that it melts.  Roll equal portions in each of the tortillas and topped with salsa (poached from your local Taco Bell).

I do what Bannock does and feel that I can use them whenever in spring and fall if temps have been cool or by day three in summer. I try to make sure the eggs are kept sfae and suurround the container with cardboard as well as surround that with stiff things near the top of the pack. I also place the cardboard egg package in a big zip lock just in case an egg breaks. Having a broken egg all over the inside of a pack for 7 days in July gets pretty stinky-Trust me I know.

Years ago, I packed fresh eggs by using 2 styrofoam cartons per dozen, and double wrapping them. I taped the cartons shut, and put the whole thing in a 2-gal ziploc. I carried large eggs. Had a few minor cracks, used them first or tossed them according to the dictates of judgement.
Now, I carry powdered eggs from a restuarant supply. I like to watch the rookies search the foodbox when I ask them for a dozen eggs.