16% protein sounds a little low for EEs/Ameraucanas. We supplement protein with boiled eggs, shrimp, salmon, sardines in olive oil, and we switched from organic pellets/crumbles to organic seed mix layer feed where we add Bee Pollen, Brewers Yeast powder, Rooster Booster for more vitamins. Sometimes I'll boil a side of turkey breast ligihtly Kosher salted in water, and cut it into pieces as afternoon treats. It doesn't need to be a lot of protein but we don't have feather-picking or egg-eating which is a signal of not enough protein. Chickens have favourite foods over other breeds and we strangely found the country of origin a clue to what our breeds like. i.e. we had a Leghorn that was the only one that liked a Mediterranean diet of tomatoes where no other breed touched them. Our Silkies love Asian dishes of brown, long grain, or white rices mixed with their layer seed and lots of cucumbers and cantaloupe. Our Ameraucanas love Turmeric sprinkled into their feed w/ sweet potatoes (not yams), dried cranberry raisins, seafood, and grains/seeds like oats, sunflower, corn, wheat, quinoa, etc. Their breed origin seems to dictate their favourite foods. Our chickens eat everything we set out but they clearly have nutritional favourites and we can't help noticing the coincidental favourite country foods where these breeds were originally created.
I think the egg rolling tray with fine grate so the chickens' beaks can't peck through is a great fix for your situation. And nothing is expensive but necessary where chickeneering is concerned. Those egg tray nests look cleaner and well-built to last compared to traditional wood boxes.