I have staggered hatches all the time. I have a 600 plus egg incubator and am always adding eggs (daily in fact). I have three styrofoam incubators (various brands) all still air. I have to check the calendar daily to see which eggs need to go to the hatcher. I put the eggs in the "hatcher" and the humidity is always cranked up. Once the chick/poult/keet hatches, I then put it in a styrofoam incubator to fluff. The humidity in this is dry. That is no water is added. After 24 hours, they go in the brooder.
I have anywhere from 1-5 hatchlings a day. This system has worked well for me for the past year and a half.
When one of the hatchers needs cleaned, I load all the eggs in one of the other, clean it, then start loading it with eggs from the incubator when it is their time.