We have a broody box--a small hutch thing with an attached run. When I had one broody for about a week and didn't want to break her, I would move her at night into the broody box on some golf balls. If she sat tight for another week or two and the stress of being moved didnt' break her of being broody, I would wait until around midnight and stick the chicks under her in the dark, using no lights. When I'd come out in the morning, I'd have pecked and dying chicks. I decided, never again.
I don't see anything wrong with what you did. That's always worked for me. I did had a hen that hatched 8 chicks and killed three of them. She raised the other 5 OK, though she was not my best broody in raising them. She kept getting them stuck on the other side of a fence by going out of a gate and turning the corner before all of them got out. Some would follow her but some would try to follow her along the inside of the fence. The dominant rooster would go over and watch over the separated chicks until she finally figured out how tp go back and get them. She pulled some other dumb tricks too. She just was not a good broody. All my other broodies have done fine with the ones they hatch and the ones I give them.
These were chicks she hatched. There was nothing obvious about why she decided to kill some of them. They were all mixed colors and everything. Sometimes you just get a broody who's instincts are just not right. I think that may have happened to you. Just a bad broody with poor instincts. I really don't think waiting longer would have made any difference.
Also, I've had cracked eggs about half the time I had a broody hen. Those are the ones likely to stink. I don't know why my hens would be harder on the eggs than other peoples' hens. They are by themselves, and do manage to hatch most of a clutch.
Yeah, if they crack just a bit the bacteria can more easily get in. That's a logical observation. I occasionally have some that crack. I think sometimes they are thin-shelled or have microscopic cracks and the broody cracks them by stepping on them when she is turning them or getting on or off the nest. It's surprising how tough most of the eggs are if you see how a broody mistreats them. Once,I think the broody cracked a couple when she was fighting off a snake that wanted to eat the eggs out from under her. I did not see it, but I think that's what happened. That one was a good mother.
If I see an egg that is cracked, I toss it. Some people melt wax on it to seal it, but I just toss it if it is under a broody. I'd be concerned she'd rub the wax off. I have not had that happen in an incubator yet, clumsy as I can be. If I did, I might try the wax trick.
Laturcotte1, I'm glad that chick is doing well. I really like to see a broody with chicks. They are a joy to watch.