It would probably work but air circulation would be the issue. Those developing chicks need to breathe through the porous shell. The later in the incubation cycle the more they need to breathe. Keeping that gunk off is important too.
What you are proposing is the simplest way, which has a lot going for it, but I’d be real nervous about opening the incubator that often and the eggs being able to breathe.
I don’t know which incubator you have or how many eggs total you have, but could you possibly rig up something else. Maybe put a hardware cloth fence across the incubator to keep the chicks off the new eggs. Or maybe make a basket from hardware cloth to put over the hatching eggs to contain the chicks?
I assume you are aware of the risks of shrink-wrapping the chicks once the eggs have pipped by opening the incubator. Shrink-rapping is something that does not happen each and every time you open the incubator, but it can possibly happen. I’ve done it before but rarely. If something is going on inside the incubator I need to fix, I’ll open the incubator during lockdown but I am aware there is a risk.
You are a little unfortunate in your timing. After 14 days the eggs don’t really need to be turned, but you’re not at 14 days. It’s something to think about if you have a late hatch.
Do you have an automatic turner that you can remove some of the rows? If so, just build a hardware cloth basket to fit over the hatching eggs and you have it made.
Can you possibly rig up something with string going through a vent hole where you can turn the eggs without opening the incubator? What I’m envisioning is a harness attached so you can lift one end of the egg carton, then later lower that end and raise the other. Just have something above the vent hole so you can tie that string off. Take the top off the carton so you only have the bottom and cut out underneath to give good air circulation. My concerns with trying to get this fancy is turning the egg carton over and spilling the eggs, or the egg carton not being strong enough to hold together, especially a cardboard one in that moist environment. You might need to build a frame to support the egg carton and attach the string to. It gets complicated fast.
The other issue with a staggered hatch like this is the humidity, especially if you are opening the incubator during lockdown. You really do need to raise the humidity when an egg pips for the first hatch but that may keep the second group from losing enough moisture. You might want to wait until you see a pip to raise the humidity. The risk of that is the pip might happen when you are away or sleeping. I wouldn’t be married to the idea that I absolutely have to raise the humidity after 18 days, but I’d want the humidity up when they pip.
I hate staggered hatches with one incubator. The easy thing is to get a second incubator to use only as a hatcher. Then all these problems go away.
For what it’s worth, this is what I use to go in through a vent hole to add moisture to my incubator during lockdown.