JP - I have a few concerns. I honestly do not think this is due to her getting ready to lay a first egg. You mentioned early on in your thread that you heard a bit of wheeziness when she breathed. Chickens are extremely susceptible to respiratory issues, and I'm wondering if that's what is going on. She doesn't sound like she has a very good appetite, and from the looks of her poops, it doens't appear she's getting enough to eat.
It would be impossible to know exactly what's causing her to not feel well, but from the pics of her, she does appear to be under the weather. A few comments and suggestions: remember that birds will die most quickly from dehydration, then lack of nutrition. So, my suggestion would be to remove her and bring her in. Bringing her in for a day and then back out isn't going to help - you REALLY need to monitor her closely and know how much she's eating and pooping. That's imperative. I use a large plastic dog crate, which works great. They cannot get out, it has excellent ventilation, and you can get inexpensive cups that hang on the front of the cage for feeding in the bird section of your local pet store. If she turns her beak up at her regular feed, dry chopping some tomatoes if you have them at your grocery - chop in small bits, and mix them in with her feed. The red color should attract her to the feed, and the acidity of the tomatoes will help with gut issues - especially if she's got pieces of styrofoam stuck in her system. Mix with yogurt (all-natural, non-fat) for good gut bacteria.
DO NOT give her Sulmet - that's for coddidiosis, which she does not have (per her poop & per your descriptions). I'm a big believer in no antibiotics unless absolutely necessary, but you have to make that decicion. I would add a pinch of electrolytes/vitamins to her water, but only give for a few days (no more than 3 days in a row - electrolytes can be harmful for more than 3 days in a row).
If you can get ahold of a better cage so that she cannot get out, that would be idea. Keep her warm and dry, and monitor, monitor, monitor! Don't take her back out until she's completely back to normal; you could be taking a step forward, and then two steps back by going back & forth with her.
Also, if you feel she's definitely not eating enough, pick up some baby bird handfeeding formula (most pet stores have it in the bird aisle). It's for hand feeding baby parrots, and it's a powder that you add water to. If she's eating at all, mix some of the baby bird handfeeding formula in with the tomatoes and yogurt. It's loaded with protein & vitamins that are excellent for chickens that are nutritionally lacking. Plus, they do seem to like it.
I think a good plan of attack would be to first get her to eat as much as you can, and drink plenty, as well. Really listen to her breathing, too. If she's rattling/wheezing (this is called "rales") there could be a more major, underlying issue. Please keep us posted!