Congratulations on your excellent decision! Chickens and cats are the best combination.
I'm not sure about your cats, but there's no way I'd put fewer than two doors between my indoor kitties and those small, rustly, peepy things that smell like chicken. You'd probably have to engage in animal cruelty to traumatize the cats enough to stay away from the chicks, and even that might not work if you weren't around. I suspect this because I had chicks in my house starting in early June, and one or the other of my two cats were posted outside the room with the brooder in it twenty-four hours per day. They looked like they were just going about their business, but every grooming session and nap just happened to take place right against the door to the office where the chicks were.
They might have been too timid to do anything even if a peep did walk up to them, being indoor cats, but they've tag-teamed lizards and rodents to death when I wasn't home, and they did it without ever reaching them. If a chick were ever trapped like that, the stress might hurt her even if the cats didn't. If, on the other hand, the chicks are big enough at eight weeks to be intimidating to the cats, there's the possibility of an infectious bite or scratch if the cats got frightened and lashed out. I'm imagining a scenario in which a cat gets the lid off of a brooder and falls in, or two chicks fly out of the brooder and scare a cat sitting next to it.
I think I read that, once the chicks are fully grown, the cats will leave them alone and the grown chickens will return the favor. At this stage, though, they're probably all still in danger, especially if you've got a hefty or playful cat and pullets who practice flying without looking around first.
Can you put a lid on the brooder for the chicks and leave it inside a closed room? That way you'd have to forget both the lid and the door for the cats to come in contact with each other. In this weather, you could probably move them straight into a predator-proof coop, right? That's the way to go, in my opinion, because you don't have all the dust and poop in the house. Just a thought. Cleaning out a brooder and kitty litter all the time gets old fast
Edited for grammar. Sigh.