Cochin setting and creating a problem!

[Buns]

Our cochin hen went to setting and had 16 eggs under her. Fine. Except that although there are other cochins in with her and although there is another nest for them to lay in, they are apparently laying in the same nest. She now has 24 eggs under her, which is rediculous. When they are even finding time to lay in the nest escapes me, but they are managing. Although I can go down and mark the eggs beneath her to identify them from the newly laid, I am wondering how long she must set on them before incubation ensues. I would like to keep some of the eggs to put in the incubator, but if the eggs have already begun the incubation process I am assuming it will kill them to return them to a cooled state. I do not own my own incubator and I drive forty minutes one way to get my eggs to the lady with the incubator who hatches for me.
So, how long do I have to find the newly laid egg and get it out from under her before the egg is ruined?
If I move her to another location during the night and put the eggs beneath her, will she be happy when she wakes up and finds herself moved or will she abandon her eggs? If I do this, how large of an enclosure must she have, and should she be away from other birds, where it is quiet?
Thank you for any help.

 

[andalusn]

I have a Cochin that has been broody since Feb 2010. She recently finished raising up her last chick. Back to sleeping next to my rooster and who knows what she will do next. Almost right on time to start again. This hen steals eggs so we built nest boxes to try and isolate her. Nothing doing. If a hen wants her spot she gets off the nest, lets them lay their eggs and then climbs back in. I simply pick her up, take out what I don't want to leave her with ( I dated the eggs) and put her back. Does not phase her and eventually she hatches her chicks.