You are overthinking this one.
The differences between the two specs are primarily in the MAP (Maximum Average Pressure), freebore diameter, freebore length, and leade. 5.56 NATO specs are not achieved through the dies, they are achieved through the loading recipe. So what you are asking about is essentially an invalid question.
Case wear can be reduced by carefully tuning headspace, but this is not done through blindly full length sizing with a die. It is done by gauging your individual chamber and sizing down a specific amount to set the shoulder and headspace exactly where you want it. This is generally not a recommended practice for semi-automatic ARs. Single loading rounds into an AR for slow fire match shooting is a different story, as you take magazine length and reliability of feeding out of the equation.
Lake City brass is very high quality and stronger than, say, Federal. However, it's not due to case thickness. It's due to quality of the brass and proper annealing. The requirement to load down for military brass due to case thickness is more of a concern for the .30 caliber service rounds, not 223/5.56.
Lastly, do you have 5.56 NATO load data? Where did you get it from? Nearly all civilian load data for this cartridge is limited to the 223 specification for safety reasons. Handloading to full 5.56 NATO pressure is unnecessary and unsafe unless you can gauge actual pressure. Most of us do not have access to pressure testing equipment to do that.