Higher protein CAN cause egg binding, due to the calcium drain that the extra blood acid levels cause. This is also a well researched fact.
The phytoestrogens and other hormone altering substances (like the glycophosphates the soy and corn were grown with) do cause an increase in the natural egg production. Phytoestrogens do not directly increase estrogen, but estrogen and the other related hormone rates in the female body are largly determined by nutrient availability, and copper levels. Since phytoestrogens are so close in form as they break down they instantly provide the necessary ingredients, thus artificially raising the resting hormone rates. Many of the ingredients in commercial grains are very high in these things. This was done on purpose as it was not only cheaper but also increased the laying rates of the hens. The resulting hormonal drive for faster egg production can be very hard on the hens body, even with optimum nutrition her digestive system often cant keep up, and will end up cannibalizing her other ovum to provide the missing nutrients. This combined with laying faster than the necessary parts cam heal means she ends up stopping laying sooner than she would theoretically have. This is also closely tied to breed as you have said since some breeds naturally have a higher laying rate they can sustain or a higher amount of ovum, or more effective digestive system ect. Commercial layer feed is designed for optimum egg production, not necessarily health.
The problem is that nutrition is so complex that to compile a completely new and higher health feed that is somehow also affordable would take an intense collaboration between an avian vet and nutritionist. So while it's theoretically possible to compile your own, it would be pretty difficult to make sure you got it completely right.
The better and less risky way is to simply use the hens own body to help, by offering a high variety of nutrient dense but low calorie foods in addition to layer feed. This is because, as we all well know, chickens are like toddlers. They eat what tastes good before what has the right nutrition. High nutrition foods like bugs, legumes, and greens offer all the nutrients, but are not so tasty they are likely to overeat and not get the variety they need. Even a toddler will get sick of their favorite food and want more variety (because they body says i dont need this, i need that) if it isnt a calorie dense one like cake. Fruits and sweet vegetables and grains are the true treats and candy.
By feeding high nutrient foods like legumes and bugs and greens in a high variety in addition to their layer feed you can let their body get what it is crying out for while not exposing them as much to the damaging commercial feeds or risking overdosing or being too deficient in anything. A hen is not going to overeat greens or beans. 70% layer and 25-30 high nutrient snacks is the accepted (with the remaining optional 5% being the "junk" like fruits and grains), but since we are also advised to have food available 24/7 that really ends up more like having layer feed on hand all the time in surplus and offering the high nutrition foods in a 1/4 c per hen per day, less if they get to free range. With a small scattering of the treats every once in a while.
If you are only adding one non layer feed food, with the goal of increasing the protien, then beans would be a good choice. Having higher amounts of the high nutrition snacks offered, with the 24/7 feed as an option is pretty much never going to cause a problem unless your variety is low and they cant free range/forage. Your body and theirs will start to reject the idea of foods that you are higher in a nutrient than is advisable for you to eat, IF the high calories arent there to sweetener the deal.