I bet the way to increase the NC is to do the counter-intuitive thing.  Let the top 1/3 by stake capture half of the rewards, but split the rewards equally.

At first, I thought this was a terrible idea, but splitting rewards equally among the top third by stake likely incentivize more participants to reach that threshold, reducing the dominance of large stakeholders. This change encourages a more distributed stake, which could ultimately improve the Nakamoto Coefficient by increasing the number of independent actors securing the network.