I knew one of the experts I follow would remember something about tests or trials of other chicken owners. I suspect you're right - adding protein might alter the egg size and overall calories. But I've gotten a few really good ideas. And thank you - I believe my issues are resolved - I'm just trying to regain range of motion, and muscle mass, which is tougher for older men (yup -- man-o-pause...)A few years back I read about a guy that was trying to start a business of selling eggs enhanced by what the chickens ate. I can't remember the details, maybe giving them an oregano flavor by feeding them oregano. He was trying to flavor them. He was also trying to increase certain nutrients like they do with Omega's. One thing I specifically remember was calcium. He was trying to increase the calcium content of the eggs but it did not work, the shells got real hard though. The article did not mention the damage the extra calcium could do to their internal organs. I tried searching for it and could not find that article.
I think you'd run into the same issue with protein. You would not get a higher percent protein per gram of egg, you'd get larger eggs. A larger egg will have more of everything, protein, fats, iron, and everything else an egg provides but that's just because the egg is bigger.
Good luck on resolving your issues.