Elgersma's treatment conflates ass-backward(s), bass-ackward(s), and backward(s)-ass as equal variants, but the history of these terms is rather complex. We can assume that ass-backward(s) came first, which was then euphemized through metathesis as bass-ackward(s). But while ass-backward(s) isn't attested by the Oxford English Dictionary and other sources until the 1930s, the spoonerism bass-ackward(s) can be found much earlier than that. In fact, it goes all the way back to the 1840s, when a young Abraham Lincoln was practicing law in Springfield, Illinois. As first documented by Emanuel Hertz in The Hidden Lincoln (1938), Lincoln wrote a note to a bailiff in one of the Springfield courts, and it was full of spooneristic humor. (It's unclear whether Lincoln came up with it himself or if he was simply repeating the work of another wag.)
"He said he was riding bass-ackwards on a jass-ack through a patton-cotch on a pair of baddle-sags stuffed full of binger-gred when the animal steered at a scump and the lirrup-steather broke and throwed him in the forner of the kenceand broke his pishing-fole."
The bass-ackwards euphemism got to be popular enough to stand on its own, as in the January 1884 issue of The Medical Summary(published in Lansdale, Penn.), which included this from the obstetrician G.O. Smith of Odessa, N.Y.:
"I was suspected of incompetency by the friends, and I began to think every thing in obstetrical practice was going "bass ackwards" with me."
While bass-ackward(s) and the unsanitized ass-backward(s) became popular American expressions in the early 20th century, backward(s)-ass is a much later development, informed by the African-American colloquial use of -ass as documented by Arthur Spears.