Our hens have always laid at different times of the day and it looks as though these egg layers my MIL has got are much the same. I've found that a hen will lay a bit later each day until she misses a day. Apparently the reason for this has got something to do with how long it takes an egg to form.
DB, yes, the hens tend to like sharing a nest. With our Thai "gai ban" it's a pain in the butt because you have a brooding hen, and the others keep laying their eggs in the same box. A few hatch, the hen goes on her way with a few chicks, and the remaining eggs are at various stages of development, which are then eaten by my FIL.

Apparently a delicacy in some countries.

Personally I think it's disgusting, both the eating and the act of cooking eggs with a live chick inside. This being Thailand though, sometimes it's just best to look the other way.
PS: DB, what type of chickens have you got?
Don't try to impress me with your manner of dress cos a monkey himself is a monkey no less - cold fact