At first glance, nothing seems further from the Just Third Way than an obscure encyclical from the early 20th century establishing a new religious feast. At second glance, it seems even further removed, for all it talks about is how Christ is the king of the world, which certainly doesn't appeal to non-Christians, and, frankly, not to many Christians these days. Pius XI's 1925 encyclical Quas Primas ("On the Feast of Christ the King") comes across as the very antithesis of everything for which the Just Third Way stands.
Let's take a third glance at the encyclical, however, especially from a "non-Catholic" but natural law point of view.
What's interesting about this encyclical (and the Feast of Christ the King it established) is that Pius XI appears to have been integrating the political philosophy of then-Venerable Robert Cardinal Bellarmine into his social doctrine. Pius XI was a student of the political and religious effects of the Reformation, and Bellarmine was one of the key players in the Counter Reformation. He was a genius of such vast learning that some of his opponents believed his name to be a pseudonym for an entire group of scholars.
Outside of Catholic circles Bellarmine (when he is mentioned at all) is best known as the man who got Galileo "off" in his first trial. More importantly, Bellarmine was the chief opponent of the divine right of kings as promulgated by Sir Robert Filmer (Patriarcha, or, The Natural Power of Kings) and King James I/VI of England/Scotland in the early 17th century. While many people aren't aware of this, Bellarmine's philosophy was incorporated into that of John Locke and Algernon Sidney.
There was a difference, however. Where Sidney mostly got Bellarmine's philosophy right, claiming that he disagreed with Bellarmine on religious grounds but fully supported his political philosophy, Locke distorted Bellarmine's work. Paradoxically, Locke then used the undistorted version in developing his own theories — among which he stressed the importance of private property in capital as the foundation for a stable political order.
Of course, Sidney had no "patron" for his Discourses Concerning Government. Locke did have a patron. He was paid by Lord Shaftsbury for his Two Treatises on Government. Locke's distortions of Bellarmine's thought might be explained when we realize that Shaftsbury was a violent anti-Catholic. He was the prime mover behind the "Titus Oates Conspiracy" that resulted in the judicial murder of nearly 20 people, including Saint Oliver Plunkett, Catholic Archbishop of Armagh, and accused hundreds of others, including Samuel Pepys (at that time a member of parliament) and the Queen, whereupon the scheme fell apart.
Locke and Oates got pensions. Sidney got beheaded.
Some authorities believe that Algernon Sidney had more influence than John Locke on America's Founding Fathers. They would thus have gotten a reasonably accurate idea of Bellarmine's political thought, which was then integrated into the Declaration of Independence and the Constitution.
Father John Clement Rager, however, made a good case in The Political Philosophy of Blessed Robert Bellarmine (1926) that George Mason of Gunston Hall (the "forgotten founder") knew Bellarmine's writings first hand rather than merely through Sidney and Locke. Mason (who was not a Mason . . . good barroom bet, there) drafted the Virginia Declaration of Rights in a way that based it on natural law — especially (surprise!) the importance of the natural right of access to the means of acquiring and possessing private property.
The "conservative" elements of the Virginia Convention forced some changes that partly undermined this by insisting that men only become (politically) equal "when they enter into a state of society." At least they left property in, even if they corrupted this critical social good by claiming that you can own human beings.
The addition to the Virginia Declaration was clearly to preserve the basis of slavery (Mason, a slave owner, was opposed to slavery!), but Jefferson (who used the Virginia Declaration as a model) managed to retain the full natural law basis, even though explicit language condemning slavery was removed from the Declaration of Independence — and he wimped out by not including property explicitly among our natural rights.