I found a possible ship record for my ggrandmother and the children. The first names all match, but the last name does not. It shows that they traveled with a man by the name of Joseph Perlis.
What is interesting is that the Outward bound UK record shows them first names as Josef, Chaze, Aldam and Sarah, while the ship record shows the names as Joseph, Basche, Abram and Rachel, which would match the first names of my relatives. The ship was Paris, date 12/18/1893 and the destination was Massachusetts, which are matches.
As far as I know, my ggrandfather Jacob Cryman/Kramer did not return to Russia after he left in 1891. Is it possible that my family was traveling under some one else's ID?