FG, I make this quite often, and it calls for the whole egg- I've never had a problem getting the egg/sugar mixture to ribbon.http://www.davidlebovitz.com/2011/11/lamingtons-recipe-chocolate-coconut-cake/
From my experience short ribs actually taste better when cooked, cooled, and reheated. Not sure what the science is behind it, but something with the gelatin happens when this is done. It also makes it easy to skim fat. A number of recipes I've done called for this method.
Ed, I'm guessing you aren't beating your eggs fast enough. I make a Lamington receipe that calls for the same thing and I typically make sure everything is at room temp first. Then I beat the eggs at my Kitchenaids max speed and then slowly add the sugar. Also, make sure you're not adding any type of fat until after you've reached the desired thickness.
I need a non-stick pan, any brand recommendations?