Please keep us informed this is very interesting. I sure hope you get something at least one or two.
You are a step ahead of me. None of my hens are broody and I'm in the middle of building an incubator. If I understood you right the hen and eggs were in the coop with your other chickens and she was sitting on the eggs. Right?. If I understand things right, and I'm new too, the best thing would have been to isolate the broody hen and eggs. Possibly have put them in your dog crate if its at least 18 inches wide and maybe 30 to 36 long( the bigger the better ). At one end make a little nesting box. A cardboard box 12 in square and a couple inches deep will work. Put some bedding or straw, I personally like straw that I run through my chipper to chop it up a little. Either works fine. Put the nesting box in the back of the dog crate. Get a small feeder and waterer ready. After all this is done wait until evening, when your birds are roosting. Have one person take the broody hen another take the eggs to the dog crate. Gently place the eggs in the nesting box and the hen on top of them. After the chicks hatch give them proper feed and water 24/7.She will take care of all their other needs. At some point you will have to give them larger quarters, not with your other chickens. They still have to be kept warm. Ok, thats were my learning ends. I'm not sure if they need the heat lamp if they are in your basement temps are probably 60 to 70. I think it wouldn't hurt as long as they had room to get away from the heat if its to warm, that may be a problem in the dog crate.
Thats the best advise I have, I hope its right, never done it only read about it, if not someone please feel free to correct me.
You deserve a couple chicks at least for all your hard work
Bob