Okay… what I would do.
1 chose a higher protein feed that is whole grain and a good pellet or crumble feed, start mixing 50/50 and gradually transition it to 100% whole grain mix and seeds type mix. The reason I would do this is most likely they have been fed pellets or crumble their whole lives prior to you. I start my chicks right away on a mix of chick starter crumbles, seeds, grit, small whole or cracked grains, bugs and fresh fruits, sprouts and veggies… they do great and transition great onto whole grain feed as they get older.
I avoid corn based feed myself, I have my reasons, because I feed no corn my only option is organic no soy as well. I am not anti soy and organic does raise feed cost just so you are aware. I have hand mixed but it takes research, creativity in getting nutrients and lots of hunting around for feed ingredients. I did it because at the time no one in my county sold corn free chicken feed… it was an adventure... good premixed feeds have made my life easier.
2 supplement water with probiotic, electrolytes, oregano tea, or poultry vitamins for water (ACV only if your watering system has no metal.. vinegar will leach out metals of waterer into water and hurt your birds).
3 add lots of fruits, veggies, herbs, spices, sprouts, greens, kitchen scraps, seeds, seaweed, bugs, worms, dried and frozen shrimps/fish, liver, other protein sources to diet… if your lawn is not treated they usually like grass clippings too. Cottage cheese even. Chickens are omnivores, never forget that when thinking about their nutritional needs.
4 offer grit and oyster shells
The Eggs for You
If I was worried about their eggs health for my end use.
I would eliminate corn as it is linked to cholesterol in animals such as farm raised fish and cattle. Different countries use different grains to feed chickens and is probably why nutritional data from Asian countries is different from Western countries. What you feed the hens is reflected in egg taste, yolk colour, yolk consistency (my chicken produce eggs that are always bright yolk and the consistency is not like water whereas the store ones are always pale yellow and the whites watery), and end nutrition to you. Junk feed = junk eggs for you is my philosophy on eggs, even organically fed commercial chickens may not be getting proper nutrients for best egg quality for you. Your goals here should be proper nutrition for your birds first and lowering bad cholesterol causing elements in their feed... think heart healthy for them = healthy heart for you too. You want good fats in their diets via good sources. A little corn is okay now and then but should be just a treat in my opinion, not the daily feed.
I would document the eggs they lay as follows as I change their feed…
weight, photo and inspect uncracked eggs, crack eggs (thin or thick shell… do I notice a change in shells), look at yolk colour, and egg white consistency, number of eggs flock lays daily... if it is possible to match eggs to individual birds I would probably do that too… to help gauge how each hen is doing.
My expectations based on my flock keeping experience and comparing my bird’s eggs to friends flocks eggs who are on different diets and store bought organic and non organic eggs is you should see a gradual improvement in egg shell thickness (the eggs should get dang hard to break), egg yolk should get bright, whites should thicken up. My birds tend to have super bright dark yellow yolks, thick whites, hard shells regardless of breed but then my feeding goals are to feed them to live long to the best of my ability, in addition I allow them to free time in my yard, they have a big communal pen as well, so lots of exercise potential, sunshine, foraging time on top of me doing my best to feed them well. I have had my ups and downs in learning what my flock needs too, so expect you might have to tweak the diet as needed. I learned some of my breeds needed more protein early on to prevent them craving new feathers of fellow birds and egg eating… I try to always get extra protein and vitamins in them during molting for example on top of normal feed.
I think you will notice the improvement within a month. If your worried about medications or something like that probably a thirty day waiting period would be good.
PS you can crush the shells and scramble the eggs you crack open cook and feed back to them, it won’t hurt them and will just be extra supplement. Yes there might be trace elements in these eggs but by the end of a reasonable wait period it should be okay. Always cook the eggs never feed raw or shell in such away they know it is eggs… they will start cracking and eating own eggs... eggs are yummy.
Ethical and Religious considerations in feed… okay if this is an issue you need to be very honest with yourself about chickens not being humans… so please consider their nutritional needs first… there are ways to do everything but make sure you choose feeds after understanding their nutrition a bit so they stay healthy. You are keeping feathered dinosaurs who in nature forage for lizards, worms and bugs on top of wild seeds, grains and plants. Chickens are a Kosher and Halal food source both from eggs and meat. (Disclaimer I am not a rabbi, this is my understanding) To be Kosher your chicken must have 4 toes, three in the front one in the back. What a chicken eats does not make the chicken meat or eggs not Kosher or Kosher… it’s the fact it meets the rules in the Bible/Torah. The religious rules even state animals do not need to be fed human food… you can of course, but it is not an expectation or even practical for society or nutrition of the critter. Big Kosher egg/meat commercial facilities feed their birds special diets to make their life easier… Passover requires that 5 grains be absent from hearth, home and farm under modern orthodox rules… just easier not to feed those all year, then to purge a huge operation of the 5 grains yearly. For regular folks these grains are temporary removed yearly and returned, pets, zoo animals and livestock simply fed differently for that time period only. The main thing is if you do feed your animals non Kosher food you must keep it away from human Kosher food… for instance store not with your food. Pretty simple really. Some people do feed only Kosher human quality feed too, but then they are usually mixing feed… and the grain is for both them and animals.
I hope this helps