Here's the single's page on 45cat:
http://www.45cat.com/record/nc993554usI can't seem to dig up any more info about this release anywhere.
Edit: A-ha! I just found more info on it in Jim Murphy's new book, on pp. 261-262. Jim's research supports this being representative of the original version of the poem, which Brian and Christian then rejiggered to create "Shut Down." However, this single of "Last Drag" seems to have been released in Apr. 1963, according to the book, more-or-less concurrently with "Shut Down." Jim goes on to explain that Tony Butala of the Lettermen, who is credited with the cowrite on the record with Christian (and apparently owned the NBI label, which seems to have a catalog of exactly one release) threatened the Beach Boys with a lawsuit for ripping off what he felt to be his song. Christian felt this threatened Murry and thus shortened the duration of his writing partnership with Brian.
Just another reason to get Jim's very fascinating book.