I don't think my broody hen, who hatched out five chicks a month ago, has laid an egg yet. So I wonder if your hen was broody when you got her and maybe it has something to do with that. I'm new to the whole broody hen business, so it's just a gander.
The stress of the move could also be a factor and the high heat of summer.
Gertrude does go up to the high nighttime roost now, along with her chicks. She's the biggest hen and has no problem getting up there. Is your girl stable on her legs? Have you seen her use her wings to fly?
With all the work I did building roosts and nesting boxes, the flock didn't like the change in their environment and took their sweet time getting used to the new setup. It's possible there's something about the roosts or the method for accessing them that isn't to her liking. It's also possible she'd prefer something lower or higher.
Check the bottom of her feet for any injuries, and consider installing a custom roost just for her, away from the other roosts and maybe a bit lower. If she's not showing any signs of a health problem, she may just need more time to figure out what she wants to do herself in the hen house at night.