Oh it's never moot!
Let's see what we have here and go with it.
First, it's awesome that your bird is bouncing back. YAY! Good news is always welcome. She shell-less eggs - likely. That needs to be addressed and in a big hurry, and we'll talk about that last here as I go through your post bit by bit.
First, her weight. By this I mean more her 'keel score' - in other words, when you feel her breast bone - is it prominant, or padded nicely on each side without being TOO padded?
Five months old - yes - time to get ready for the laying. It's best to do it ahead of time so that when they do lay, they have all the tools to do so.
Are you giving them any oyster shell? Are they getting any laying feed at all? The feed you're feeding is very high in phosphorus which will not only cause shell less eggs, but start to take the calcium out of the bird's actual bones to make up for the high phosphorus. This must be fixed.
If you're into organics, at least find an organic complete feed. Grains, etc, should comprise less than 10% of their feed unless you're a feed designer. Relationships between vitamin D3, calcium, phosphorus are so delicate and must be adhered to strictly.
You wrote" 5) She is eating grains (millet, buckwheat, oat groats, barley, etc), along with grass and weeds in the back yard. I also give them fresh corn, cantelope, grapes, cherries, sunflower sprouts, and shrimp (with shells) every day as treats. They eat bugs, insects, and worms when they can, and tear up the arugala I planted for them in the garden. They regularly scratch in the dirt for bugs and sprouts. I don't give grit, since I've read pastured chickens get it on their own. Occasionally, I'll pour them a bit of my banana and berry smoothie (which they beg for), which does have a little dairy in it, but only once or twice a week, and I have been doing this for 2 or 3 months."
There's the issue. First, no - pastured chickens still need grit (just they might not use as much) because not every environment contains the variety and size and most especially hardness of grits needed for birds. Oyster shell is not grit - it's a calcium supplement so that birds can regulate their own calcium to some degree. It dissolves very quickly compared to granite grit. Grit and oyster shell should be given to any free range birds in a separate container so that they can self serve. It's very inexpensive these days to get a small bag of each (most feedstores sell the little bags now - or they're online and not too heavy to ship cheaply).
I'm less concerned about the grit than I am the diet. I see a diet that is such a lovely supplement, the best supplement you can get, but a diet that is bound to cause laying issues especially in first-timers. Please at least look into organic laying pellets or mash with a vitamin package. Birds MUST have nutrients, and it's possible that your bird will start depleting her life-dependent calcium or already is.
I hate to sound alarmist, but I've seen it way too many times. And I'd hate to have you have problems with her and the other girls.
I think that (and the added stress of heat) is the issue. Everything else sounds pretty normal except her vent, which I think is from the stress of what's going on with her right now. Plain yogurt (1 teaspoon per bird) will help that. They'd LOVE that if they like smoothies. My baby chicks attack me every time I put my hand in the cage now because they think I have yogurt. Seriously - they're vicious! lol
Despite sounding negative above, I think you've done a lot to think about whole foods that birds benefit from. I think if you adjust it to where you get an appropriate laying feed in her with a vitamin package and then give what you give for the other 10% (withhold it, leave only the laying food, except for the evening/afternoon) then you're going to have an exceptionally healthy flock. But let's get the basics down here first and then add the lovely icing to the cake.
I do hope this helps. Please let me know if I can be of any further assistance either here or email or whatever you need. It's my pleasure.