It looks like the original forum post for this story fell down the Time Hole, so I hope you don't mind if I re-introduce it for discussion. This was one of Wolfe's stories that I had inexplicably not read before, and as you said, it's classic Wolfe. There's a lot to unpack in the story, and in the controversy today over privately-run prisons and prison labor in America, as well as the resurgence of slavery in the Third World and the continuing controversy over the history of slavery and the Civil War, it remains quite relevant.
Your comments in the podcast were absolutely spot-on regarding Wolfe (echoing Chesterton) and his examination of the need for a Third Way based on a Catholic understanding of mercy and compassion, It's interesting that ransoming the captive is one of the 7 Corporal Works of Mercy, and that the Pope abstains from voting to carry out yet another, burying the dead.
The story seems to be based on several incidents of papal history, especially the 15th century reintroduction of the instutution of slavery in the New World, and the (largely fruitless) efforts of a succession of popes to end it, beginning with Eugenius IV and his 1435 bull Sicut Dudum which demanded that Christians free all enslaved natives of the Canary Islands within fifteen days under penalty of automatic excommunication; followed by Pope Paul III's bull, Sublimus Dei, which taught that natives peoples were not to be enslaved; in 1591, Gregory XIV 's Cum Sicuti, addressed the bishop of Manila in the Philippines and reiterated his predecessors’ prohibitions against enslaving native peoples. In later centuries, Urban VIII promulgated Commissum Nobis (1639) in support of the Spanish king’s (Philip IV) edict prohibiting enslavement of the Indians in the New World. Benedict XIV's Immensa Pastorum reiterated in 1741 that the penalty for enslaving Indians was excommunication; in 1839, Gregory XVI issued In Supremo to condemn the enslavement of Africans, and Pope Leo XIII promulgated two bulls condemning slavery in 1888 and 1890.
Yet many, if not most of these efforts were ineffective, as by this point he papacy had little political influence over the Spanish and Portuguese and always held little over the antebellum American south, just as the Pope in the story has been stripped of all secular powers of persuasion. One can argue, though, that by keeping the doctrine of opposition to slavery alive, in whatever diminished political position the papacy held, it maintained one of the few primcipled bastions against slavery from the 15th to the 19th centuries, until it began to take hold in other countries and sects. Ideas, like seeds can remain dormant for centuries until they find fertile soil. So maybe there is something to the belief of the Pope in the story.
Likewise, the papacy's resistance to the rising power of Hitler required a similar balancing of principled resistance to the Nazi program of euthanasia of the disabled and deformed, and the very real risk of the wholesale destruction of the Church and persecution of the Catholics in Germany and the occupied countries. Through history there has been a continual walk on a knife-edge between matyrdom and the repression or even destruction of the Church (and associated human misery) and a worldly accommodation with civil authority - a problem the current Pope is trying to balance in China. The Pope's notion that Bushnan could replace the last nun is interesting as well. If Wolfe is not using the color choice of blue ironically, could that reflect a hope for her redemption and the taking of Holy Orders? If I were to teach a class on the Catholic Imagination in Literature, this story would absolutely be one of the works assigned for reading and discussion along with Flannery O'Connor, Walker Percy, G.K. Chesterton, Evelyn Waugh, et al. A great story and a great podcast discussion. As a side-note, Sal's invitation Bushnan to upgrade his software for a nominal cost is probably the first appearance in literature of an all-too-common modern experience, as our computers continually remind us to upgrade our security software, upgrade to the most current OS, etc. (and, occasionally, we are asked to affirm that we are not robots.)