A few of my thoughts from reading this, before listening to the podcast.
I love the setting. The shipboard life feels real, with the whole class separation and the slowly degrading nature of the ship and on-board equipment. The planet, Antioch, is a great ghost town mystery, until the mystery is partially solved. The alien ship is very alien and malevolent, but not understandably so. It's just weird and alien.
I like that most of the tech is not explained, unless that explanation is sensible in the moment. It reminds me that most of us use technology we understand vaguely or not at all everyday. Much better than the, "As you know, Bob..." infodumps we sometimes get. At the same time, it all feels thought-out, not just plot-magic technology.
Father Veronica's explanation of how she thinks of free will versus omniscience was really interesting and thoughtful.
Some parts had a Game of Thrones feeling: I was trying to decide if Bartolomeo or Par was Tyrion Lannister. Pretty sure Bartolomeo is like Tyrion and Par is more like Littlefinger. I was kind of thinking that Captain Nikos was a bit King Robert Baratheon, but he surprised me by sticking around and really improving as a leader.
Also, I agree with Brandon that it reminds me a lot of Gene Wolfe's Silhouette (ok, I cheated and listened to the start of the pod before typing this up) and also the GRRM story you did a while ago, The Way Of Cross And Dragon (in the Jesuits in Space way).