For my protein, I deep condition with mayonnaise, EVOO, and a lil bit of water. Then, for my moisture, I slap on some moisturizer and seal after rinsing out the conditioner. That works pretty well for me. Maybe you can try something similar .. a not-so-heavy protein conditioner followed by a good moisturizer?
Or, if you really want to mix a deep conditioner that has moisture and protein, maybe you can use mayo in place of your egg. I've tried egg before and it's much stronger when it comes to protein. I'd recommend egg only if you want a heavy protein conditioner. HTH!