Looks like you could possibly trim the perch abit so it doesnt hang over the top of the concave... I dont really like those nest boxes, they dont seem big enough, i prefer wider boxes than higher.
The wider boxes have the concave up one end, away from the hole and it gives the parents more room in there too. Because they arent high there is no need to have the perch inside, just on the outside so they can get in.
Here are the boxes i have:
If the eggs get too cold then i doubt they will come to anything. Hope your hen settles down soon.