Yeah, the wait a week approach was sort of what I had in mind. She tried this a couple weeks earlier too, but then she stopped by herself. We should be getting some colder weather soon too, so that might help as well.
I wouldn't want to build the cage myself, since the only smart place to put it would be the ceiling of the run, and I don't know if I'd trust it to hold. Maybe I need to haul the smaller dog crate from the cottage or something.
I've tried taking her out of the nest a couple times, she can stay with the flock for even half an hour, but then she goes back. She seems to have an internal clock that says when she's supposed to go lay an egg, but the time of the actual laying gets later every day during her stretch, so she ends up spending longer and longer times in there which seems to induce this, at least that's how it went close to the end of her previous two weeks of laying every day. Now she did it for two weeks again and started spending a longer time in the nest towards the last couple days, and hasn't laid in two days.