There is so much to comment on in this story I could ask questions all night. I’m just going to make a few points.
If a hen kills her chicks you don’t let her sit again, no ifs, no buts.
The hen you put in a wire cage to break her broodiness wouldn’t have been laying eggs if she was broody. The egg laying mechanism switches off, usually after 24 hours but occasionally they may lay two more eggs but that will be it. You write you were taking her eggs every day?
Hens to sneak off and make nests outside, but to last a month as you write she would have to have got off the eggs to eat and drink. This is how you find a sneaky broody. You wait near her usual food source and follow her back to her nest.
However, if she had 28 eggs under her then she had either been laying for a month and then sitting for another or she wasn’t broody and had just made a new home away from the rest.
Here the chickens free range and I have never had a hen make a nest out in the open that has been further than 50 metres or so from her usual food source. It does take a bit of commitment to find such secretive nest builders but I haven’t lost one yet for more than 24 hours even if it’s taken me another couple of days to find the nest.
Where did you find her and how far away from where they feed was it?