Thank you, John.
UPDATE: So it appears this wasn't such a mystery after all (just a mystery to me). Thanks to Joe Notaro and Tom Interval's Houdini Magical Hall of Fame Facebook page, here is a photo of the effect, along with a description from the great Patrick Culliton:
"The Cutting a girl into eight pieces apparatus was in the Niagara Museum from its opening until the fire. I put it together (not to perform, but, to display) for the Butterfield auction. I was not impressed with the illusion which Dunninger made, and Kevin Connolly has a letter from Houdini to Dunninger in which Houdini really complains about the shoddy workmanship. He says his men had to completely tear it down and rebuild it. It was really to take advantage of the Sawing a Lady in Half fad of a few years before. Hardeen performed it, and in a very rare professional appearance as a magician, Jimmy Collins performed it (and handcuff escapes and a straight jacket escape) around 1928."
- Patrick Culliton
It's said Dunninger's original design for the effect had the assistant fully concealed inside the box. But Houdini felt this would arouse audience suspicion, so he redesigned it to display the girl's head and feet.
The original "Slicing A Girl in Eight" apparatus sold for $3,450 at Butterfied & Butterfiled's auction of memorabilia from the Houdini Magical Hall of Fame held in Los Angeles on November 15, 1999. The restored effect was resold at a Bonhams auction of Entertainment Memorabilia on June 16, 2008 for only $2,700.
UPDATE: A December 5, 1926 article in the New York Daily News reveals that the women in the box was Houdini's niece Julia Sawyer.
- Houdini's grand finale: 3 Shows In 1
- Houdini on his 1926 Buried Alive: "I like it very much."
- Ad shows Houdini performed Buried Alive in 1926 (and "Slicing a Woman in Seven Parts")