Oh yeah, I just found it on Amazon: The Men. Hmmmm. . . .no song called "The Thing". The "Church of Logic, Sin and Love" title sounds familiar though. Who knows, maybe I've got the complete wrong group! I just ordered it for $4.29. Reliving my tattered youth, I am.
UPDATE: I just dug out my tape(s) and am wondering if "The Thing" might be by Mary My Hope instead. And I'm SURE you've all heard of them, too. I'll have to listen to both to try to find it.
UPDATE II: No, it was The Men:
"Church of Logic, Sin & Love" was quite successful on modern rock stations in 1992. Half spoken-word '60s nostalgia, half Crowded House-style guitar pop, "Church of Logic, Sin & Love" offered a respite from angst-ridden grunge, but the song was perhaps too quirky to have any appeal beyond alternative radio. The track had poetic imagery -- "It's the kind of place where space explorers could have landed/Around 1963/when John F. Kennedy was in Life Magazine/And everything was aqua marine, aqua marine". . .