This nutritional chemistry is way above my pay grade, but it would appear that your customers are not unlike others who have been heavily influenced by the marketing being pushed at consumers everywhere that they are buying chicken or eggs that have been fed a vegetarian diet. Chicken feed makers are following suit and proudly marketing and labeling their feed as vegetarian.
The chicken, as you stated, is an omnivore and needs a balanced diet of building blocks of vitamins, minerals, fats, proteins, amino acids and many feed makers are reportedly using "synthetic" elements. I suspect that some of those synthetic elements are still derived from animal sources.
But the bottom line is that preventing the chicken from eating bugs, worms, grasshoppers, insects, amphibians, reptiles and andy other animal meat they possibly can find goes against one of the main objectives of a chicken's life.
I'm sorry not to be able to provide more guidance, but whenever we have this conversation with our customers we are kind and polite but if we fail to instruct them on how a chicken actually lives and what they actually need to be healthy, then sometimes, we just lose a customer. We live with that. I really cannot guarantee a vegetarian diet. The egg is a "animal" type product of bio, of animal life. This is a really tough area and I feel for your consternation. Best regards.