I'm pretty sure the dark green poo indicates cocci, but the yolk colored poo surely indicates a problem with laying, as one would assume yolk colored poo is, indeed, yolk. Chickens will have some cocci and some worms; no avoiding this if on the ground, but as a rule they are not that compromised from the cocci except as chicks. She probably needs worming, if you do not worm on a schedule, but this is not necessarily the main problem, with the yolk colored poo. And worming is rough on them if already ill. Personally, I would assume that the egg problem is the core one. And I do not know that there is much you can do about this, since you have determined there is no broken egg just above the vent that you can remove.
These hatchery chickens are bred to make lots of eggs. I suspect this is also resulting in disorders of the egg laying system. Nifty (well I think it was Nifty) recently had a necropsy done on a hen that just dropped dead. It found a cancer of the reproductive system, which was evidently not an unusual occurrence.
You probably already knew at least some of this, but maybe some will help.
I wish you and your hen well!