Origin of "Screw the pooch"

Wiktionary says this of "screw the pooch":

The term was first documented in the early "Mercury" days of the US space program. It came there from a Yale graduate named John Rawlings who helped design the astronauts' space suits. The phrase is actually a bastardization of an earlier, more vulgar and direct term which was slang for doing something very much the wrong way, as in "you are fucking the dog!" At Yale a friend of Rawlings', the radio DJ Jack May (a.k.a. "Candied Yam Jackson") amended this term to "screwing the pooch" which was simultaneously less vulgar and more pleasing to the ear.

The unsourced part about Rawlings and May was added by an anonymous user in 2008.

Since then, this information has been repeated on numerous websites. While it's quite plausible that "screw the pooch" is a euphemization of "fuck the dog" (Green's Dict of Slang agrees), the rest of this seems a little dubious. Various sources suggest that there was indeed a Joseph L. "Jack" May who DJ'ed "The Candied Yam Jackson Show" on the Yale radio station WYBC when he was an undergrad from 1947 to 1951. And Rawlings is mentioned alongside May/Jackson in this article about the Chi Delta Theta literary society in the Feb. 7, 1950 Yale Daily News:

"The chorus of the gods at dinner," as the motto of Chi Delta Theta requires, was sung and played, soothing the more savage breasts, by David Chavchavadze, 1950, "Candied Yam" Jackson and Med Bennett, 1950, and John Rawlings, 1950.

Anyone have firmer evidence about the origins of the phrase?

(Question from Ben Zimmer via ADS-L.)

Tom Wolfe wrote an excellent book about the origins of the space program, which was made into a movie, The Right Stuff. If you read the wiki entry on the movie, you'll learn more.

Early competition between test pilots (true heroes) and the first astronauts was intense, with each trying to prove they were braver than the other. Cowardice or loosing control due to fear was nicknamed screwing the pooch.

Gus Grissom always wanted to be a pilot. He flew over 100 difficult combat missions in an F-86 in Korea, became a test pilot, and was chosen by Nasa as one of the seven original Mercury Astronauts in 1959. Astronauts were confined alone to a tiny Mercury capsule, with a small round window, and a lot to do manually. The pressure was great on them.

Gus's first space flight was somewhat less than a complete success. Upon splashdown in the Atlantic Ocean, the 70 explosive bolts which held the hatch in place inexplicably exploded prematurely, forcing Gus to evacuate the capsule and swim while the rescue helicopter frantically tried to save the capsule from sinking. It was not successful, and Gus nearly drowned while the capsule (which contained a lot of information) sank to the bottom of the ocean, never to be recovered.

Although his fellow astronauts supported him in every way, and a NASA inquiry led to the eventual conclusion that the explosive hatch blew of its own accord, Gus never recovered his stature with the public or the media.

Gus went to his grave unflaggingly insisting that he did not screw the pooch, which was test pilot jargon for submitting to panic. "I didn't do anything. I was just lying there and it just blew, said Grissom." However, the media painted him as a failure, a coward who panicked and blew the hatch in an attack of claustrophobia.

"The phrase screw the pooch itself was derived from an earlier phrase that was quite familiar to those of us in the service in WW2. I was a Fire Control Computer technician (Fire Controlman) in the US Navy 1944-1946.

"Anyone who has ever been in the military has spent an inordinate amount of time in a 'stand-by' formation waiting for someone to get the orders to start some activity. Many man-hours were spent in an activity that was commonly known as 'Effing the dog.' Back home in civilian life this was cleaned up to the slightly more acceptable 'screwing the pooch."