This may not be the most popular suggestion, but I was thinking that if most duties were doubled, ie hatch 20 eggs instead of 10, that this would take us basically twice as long and thus reducing the time we are waiting for the cooldown. Maybe a combination of this and 4hr cooldown.
One other suggestion, get rid of quest/exploration in duties. I think most reroll 50 dragons in exploration as many are at a point where they cant progress. Also 50 eggs from quests was alwaysannoying as well as it served as a brake on exploration early in game. Let us get them however we choose