Green’s Dictionary of Slang

(US) a xylophone, thus woodpile man, xylophone player.

1935		Charleston (WV) Daily Mail 27 June 8/8: I knew a ‘snake charmer’ is an oboe, a ‘wood pile’ a xylophone, ‘phone booth’ a bass fiddle and ‘African harp’ a banjo.
1938		Eve. Sun (Baltimore, MD) 19 Dec. 21/4: Woodpile man: xylophone player.
1941		Pic (N.Y.) 24 June 24: What Do You Know About Music? [...] What instruments are sometimes referred to as ‘woodpile,’ ‘plumbing,’ ‘licorice stick,’ ‘88,’ ‘skins’?
1951		Time 22 Oct. 69: Red Norvo kept salting his half-hour stands with such tunes as [...] he used to rap out on his ‘woodpile’ (xylophone) with Paul Whiteman’s band 20 years ago.