Interestingly, in my Audubon Society Encyclopedia of North American Birds (1991 edition), "Lord God Bird" didn't even make the extensive list of "other names" for the Ivory-bill:
Caip; Indian hen; ivory-bill; kate; kent (from call notes); king of the woodpeckers; logcock; log-god; southern giant woodpecker; white-billed woodpecker; woodchuck; woodcock.However, "Lord-God" does appear in the list of "other names" for the Pileated Woodpecker.
From a marketing perspective, I have to agree that "The Lord God Bird" or "The Grail Bird" are better nicknames than "caip" or "woodchuck".