Substitute whole eggs for egg whites
That would be a difficult substitution, because egg whites and egg yolks have very different roles in baking. It is even worse that the recipe is already not a robust standard recipe, but a lowfat, low-sugar recipe, where all tolerances have probably been used up in engineering a texture which works with the current substitutions. It is doable, but it is not a matter of "one look and one can tell what will work out", you would have to go through a process of trial and error. 

To kick off your recipe redoing, start with the eggs only. The closest results will be by obtained by using two whole eggs. This will certainly give you a different outcome than intended by the author, it will be wetter, and may bake differently. If you don't like it that way, for the following attempts, start reducing the applesauce in 10% steps. This will dial back on the wetness problem. If that doesn't work and the change in applesauce amount only moves you between a dry, crumbly texture and wet, soggy texture, you might have to dial back to using only one whole egg and adding one or two egg whites, doing half the substitution so to speak. Another improvement may be gained by adding more fat back in, for example in the form of using cocoa powder with a high fat content. 

In the end, it also depends on your personal preferences. For some people, only the best texture will do, and then the task is very difficult. For others, any brownie is a good brownie, and you can just drop in those whole eggs and enjoy.