I don't have the set-up you are looking for so I cannot help you there. However, I noticed you mentioned a week or so. That is not long enough. When a hen is mated, she normally will stay fertile 2 weeks. It can be less and it certainly can be more. Many breeders wait three weeks after isolating a rooster with the hen or hens to make sure that rooster is the father of any resulting chicks. There have been reports of eggs remaining fertile for 3-1/2 weeks after a mating, so some breeders wait 4 weeks to be absolutely certain.
It is different if no rooster has been with the hens, of course. Then you don't have to wait for the old rooster's sperm to clear. The new rooster will be the only possibility. It normally takes 2 days after a mating for the eggs to be fertile. It takes about 25 hours for an egg to make its way through a hen's internal egg-laying factory. It can only be fertilized during the first 15 minutes of this journey. So the egg is not fertile the day of the mating, may or may not be fertile the next day depending on the time of the mating and the time of the egg laying, but the following day the egg will almost certainly be fertile.
Good luck!
