I love the recording "Rivers of Delight", by the Word of Mouth Chorus in Vermont. It has a couple of "arranged" songs, i.e., adding a part with each repetition, so may not be strictly kosher (so to speak!) but it's beautiful.
Burke, the Sacred Cow Harmogenizers are (were?) a group of shape note singers in Seattle who meet more or less regularly to sing and have a pot luck. When I belonged, in the mid to late 80s, we had one performance a year, at the Northwest Folklife Festival. We did a little bit of irreverent lyric modification, but mostly sang the songs straight, and had lots of fun. I miss the singing.

Aloha,
Mark