The best time to move a broody is definitely before you give her the eggs -- and then wait 24 hours or more to be sure she will accept the new spot. I did once move a broody when the eggs were nearly ready to hatch and got away with it, but don't think I would try that again. I think if an egg hadn't been peeping, it would never have worked.
Chickens are relaly unpredictable things, though. What works for you ma never work for me, and the way my flock reacts to change is probably going to be different from how yours does.
I have put day old chicks under a broody and had her accept and raise them I also had one reject them, but that time I put them under her during the day. It might have worked if I had done it after good dark, late in the evening. Otherwise, I've never tried it with brooder raised chicks unless they were all adult sized. I've had several broodies raise their chicks in with the flock, though, and there was no problem when the mama decided she was no longer their mother, returned to the roost by herself, and started laying again. The chicks tended to stay in a bunch off to themselves and sleep huddled on the floor for a while, but in time joined the flock on the roost and foraging. It;s the other hens who wil try to bother them, and who the mama will run off, but this has always stopped before the mama gave up mothering. Roosters either ignored the chicks or helped their mama care for them.
In the old days, many a hen made her nest in the hayloft and the farmer never knew it til the chicks jumped down to the barn floor several feet below at one or two days old -- without injury. I wouldn't worry about the height of the nest box. It's true that the chicks won't be able to jump back up to it when young, of course, but the mama will simply cover them where they are. I just throw a little fresh hay around so she can make a good nest, usually in a corner somewhere. She willl probably lead them to the roost before she stops mothering. I do have a separate "broody room" in my coop now, with chicken wire walls, and that has worked a couple of times -- but I only use it before hatch, so the mama will have peace during setting, and the eggs don't get knocked around so much, mama doesn't return to the wrong nest, etc.
Like I said, the only thing I do ehen they hatch is move the layer feed out of the coop -- well, and scatter a couple of bricks so they chicks can reach the food and water.