First of all, thank you for that cogent exposition.
Rawls did explicitly state that he was situating his conceptual construct in the “liberal tradition” — basically, liberty and equality as the ‘twin pillars of justice’. Wouldn’t that serve as an answer to the question of “P*” for him?
From the first time the word was uttered to today, ‘justice’ has been based on beliefs, whether secular (ideological) or religious (theological). Beliefs divide people into ‘us’ and ‘them’. It is impossible to arrive at a universal principle of justice via beliefs.
Out rational capacity is the only possibility for the commonality that justice requires. To keep justice free of beliefs, both its determiners and its referents must be located within material existence.
I think I have successfully accomplished that task. If any reader’s curiosity exceeds one’s skepticism, a brief summary of ‘real justice’, as I have come to call this approach to justice, is here in Medium (a “5 min read”).
This isn’t something I came up with this morning. I have spent my adult life working on it, reading and studying history, philosophy, and economics within academia and outside it, including earning an M.A. in economics (with my Thesis in political economy, where economics and philosophy intersect, which included a Review of the Literature of the academic debate concerning ‘distributive justice’ that was initiated by the publication of Rawls’s book).