These look fantastic, too! As for your substitutions, I'm going to make some educated guesses here. Among other things, eggs bind, leaven, and add flavor--usually richness. You could try omitting one, but you might end up with denser, less rich cake. Adjusting the oil, applesauce, and carrot amounts will change the moisture in your recipe. If you do reduce the oil, it may not stay moist as long, but if you eat it up quickly, it may not matter. Adding more applesauce and carrot, though, may make your cupcakes a bit mushy. It would be interesting to try, though!

Hooray for fitday! I used to use that, too. =)