I know it sounds weird, but egg-free mayonnaise (use 1/4 cup) is a great substitute for eggs in meatloaf. The mixture of olive and stabilizers provide the binding that eggs would do and I promise you won't taste it at all. You can also leave out the eggs all together. The stuffing in this recipe helps bind the loaf together enough that it will still hold its shape. You may not be able to slice it as cleanly, but it will still be delicious!