In my humble opinion this is more a 'tongue twister' than 'vocal gymnatics Maybe even phrasing.
A perfect example of Elvis 'vocal gymnastics would be "Trying To Get To You" Listen when he sings the line "it wouldn't mean a thing". The word 'thing' is almost like a yodel. Also the line "you really loved me true". He does the same thing with the word 'true'.
As far as 'tongue twisters' are concerned how abot the line in "Got A Lot Of Livin To Do" ? "There's no one I'd rather do it with than you" Loses me everytime.