My son has all these food allergies, chief among them being egg -- which is in everything! More ...
So we've been experimenting with replacing eggs in recipes. Sometimes, it works. Sometimes, it is a disaster. In one of Paula Deen's cookbooks, she listed "2T corn oil and 1T water" as a replacement for one egg. We've found that works really well -- or in recipes which already have applesauce or banana, I just add a little extra fruit. We've also tried EnerG egg replacement, but like the applesauce or banana or oil replacement better. The applesauce worked great in your recipe!