I've heard the Amen cadence and the other two chord progression cadences before and I love barbershop endings which, to my surprise is also part of white male gospel singing, male Southern gospel quartet singing! I've never heard of the two being combined together until l heard the ending of the Mervin Shiner and The Jordanaires 1951 recording of Get Together with the Lord! It's a two chord progression cadence that has a barbershop ending in the middle of the two chord progression cadence! Are there other other recordings, videos of white male gospel groups, male Southern gospel quartet groups singing that has a two chord progression cadence that has one of the barbershop endings in the middle of the two chord progression cadence?
I'm sure what counts for you as a "barbershop ending," but I did a search on some of the old men's choir songs, and I found this which might be a match: Doyle Lawson - "Climbing Up the Mountain"
It might help your search to know that both barbershop and men's quartet gospel singing were innovated in the African-American communities, where the same group might sing in the barbershop on Monday and in the church choir on Sunday. If you can find some of the original "Blind Boys of Mississippi" and "Blind Boys of Alabama" recordings, they might be a good resource. This song has the Amen cadence --you'll have to let me know if this is the barbershop flavor you're looking for: Blind Boys of Mississippi - "Leaning on the Everlasting Arms"
I have a last candidate, but it's a bit eccentric. This live version of the Band's "The Weight" song (from The Last Waltz) promises an Amen cadence at the end, but then it never resolves it! One of the most baffling endings in all popular music. It used to drive me crazy, but over the years I've come to love it. It's a good echo of the off-kilter religious themes in the lyrics.