One of my hens went broody so I decided to let nature take it's course.
She laid three eggs. Soon there were a dozen eggs under her, then I saw another hen laying beside her. There had gotten to be so many eggs that she needed help setting on all of them. They have even recruited the guinea hen, and other hens, to set for them so that they can take a break!
At present here are about 20 eggs they are setting on!.
So, if I am reading you correctly, this sounds like you have a minimum of 4 hens for 20 eggs. (?) If so, that's not too much at all. Two good hens can cover 20 eggs or even more reliably.
Now the problem. The first three have hatched, but we didn't know when. I noticed that because the hens were busy setting, they didn't show the new ones how to get food and water. By the time I had a chance to make a box for them, and collect them, one of them had already expired. The other two are safely eating and drinking chick starter in the box inside the house.
A worse scenario is where one or two hatch and every single hen abandons hatching or almost-hatching eggs to try to care for the one or two babies that have hatched. This is pretty common. Also, just because they brood together does not mean they will co-mother and violence outbreaks are common too, with the chicks caught in the crossfire.
However, the fact that no hens looked after the babies says you already have some proven duds among them. The hen who has been sitting longest should have looked after the babies, and failing that, another one should have responded... But none appear to have done so. This is a likely sign of weak or absent maternal instinct. We've totally bred it out of some breeds, and in the ones who retain it, every single aspect of maternal behavior can be graded on a scale of 1 to 100 for weakness/strength, presence/absence, etc --- the variation is massive. Plenty of hens are only good for brooding, they cannot mother.
Unfortunately, "letting nature take its course" applies to wild animals and can never be taken for granted in domestic animals, because mankind has tampered with them so deeply over thousands of years. Instinct is rapidly changeable, not immutable at all. All you need is 5 to 7 generations to change something otherwise considered fundamental.
Multiple broodies in one area is a very high risk situation for babies though, so possibly no hens looked after these babies because they were crushed or killed early. Even if killed when wet, and pulled from the egg, they will dry out all nice and fluffy like they were alive.
But what about the other eggs?
Q: Should I take the eggs out from under the hens when I don't know what day they are? or should I just keep checking for new chicks to rescue?
Checking for more chicks to rescue won't save them all, but it's one way you can try to control this situation.
Hatching under a mass of hens is very hazardous. Quite often, when they hear one hatching, the hens on the furthest point away from the hatcher will start rolling eggs towards them, or pushing towards the peeping, and this constant rolling and egg-swapping and shifting kills the babies as they try to hatch. Separation is the safest bet.
This is how you'd probably be best to go about it: Use a good torch at night to see how well developed the eggs are. Bring a lead or graphite pencil, nothing toxic, no permanent textas or inks, and mark the eggs in some way which will group them according to development stages, as in make them easy to identify at a glance. Then just put them back for now. Gradually, whenever you're able, over the next few days get other cages ready so you can separate hens with clutches of differently aged eggs or babies. It's not hard to make little broody cages out of scrap metal etc, even if you've never built anything in your life. The further they are from one another, the better, as they may abandon a hatching clutch to go find the source of distant peeping noises. Some hens will also become highly aggressive and once the babies are hatched, if they can see another hen, they will spend all their time stalking up and down against the mesh trying to get to her to fight --- often trampling her own babies to death in the process.
Another thing to watch out for is that any hens who panic if you go near them will likely be bad mothers and at worst kill the babies, at best teach them to avoid and not trust humans.
Q. Will the hens set until all the eggs are either hatched or too old? Or will they quite and leave the newer ones? The other hens keep adding to the heap...so they will never be finished!
What to do?
There are no guarantees, but your best bet is that this is going to be a bit of a fiasco and keep you very busy, and may kill a good few babies into the bargain if not all of them one way or another.
If all of these are unproven mothers, you most likely have some duds among them, who can fail to any degree and at any stage of the mothering process, usually without warning. They may stop brooding, leave hatching eggs to seek out unhatched ones to sit on, kill babies, abandon hatched babies at a few days to a week old to re-set and brood, refuse to snuggle or feed their babies, leave them behind instead of waiting for them, etc. Unproven mothers are work! There is no guarantee of what they will or won't do at any point. Also, just because the baby hatched right next to her, does not mean a hen will bond to it... She may kill it even if it's hers just because other hens are near. Never trust an unproven hen with babies. The dead ones you found may have been killed, it's more likely than not. If they were under 48 hours old, they did not die for lack of water or food as they don't need it before their third day.
Once you've marked the eggs you can start daily removing fresh ones and this will give the developing ones the best chance of survival. If you don't do this you risk losing them all. Changing a hen's bonded spot to another spot is difficult because most will simply shift during the daytime back to the geographical location they bonded to. They're rarely bonded to the eggs, but rather to the location. This is where a lot of trial and error comes into it.
Generally I move my hens once broody to another separate cage, during the night, eggs and all, where I lock them in for a week to make them bond, provided they don't stop brooding. All going well, after that week, they can be allowed to free range and will go back to that nest box to brood, but a few are too dumb and will just keep going back to the main cage. Without exception I have found those to be the weakest in maternal instinct, and I stop them from brooding ever again, because experience shows me they will only fail and waste chicks' lives --- and my time.
Best wishes with your broody party. 
I do walkabout a lot, lol, had a good one today actually.
