Ray's got the 240 Page right -- at least, according to Warren Page. (pages 162-163 of The Accurate Rifle by Warren Page, copyright 1973). It was drawn up by Page and Al Marcianti "on a piece of experimental ordinance brass. . ."
Winchester "rebuffed" Page's attempt to get this to a factory chambering, and he met with Remington, proposing a 6mm similar to Fred Huntington's .240 Rockchucker. Obviously, this was before the 244 Remington; the case was based on the .257 Roberts -- or, the 7mm Mauser, take your pick, since the Roberts is based on the 7mm Mauser.
The Speer Manual No. 4 (or so presented in my copy of Designing and Forming Custom Cartridges, by Ken Howell) has the 240 PSP as formed on the .308 Winchester, and that is wrong, as Ray said. It would be based on the 7mm Mauser -- whether made from that case, the Roberts case, or the .244 Remington would depend on just what it's origin date was.
Finally, I can't really remember, but I *think* the Page Super Pooper was spelled just that way, without a "o" in Super. The word "Souper" was used with a .25 caliber wildcat.