JunkYardDog: the only placeswhere Let God Be True says that Jesus died on a cross are quotations from the Scripture, that are taken out from the American Standard Version (in the 1946 edition). On pages 42 and 43, in paragraph 13 it says about the "Jewish rabbis, priests and sectarian leaders" to have stirred up "the misguided Jewish people to cry for Jesus to be impaled on a tree." So before they released the New World Translation they used "tree" instead of "torture stake." The 1952 edition quotes the Emphatic Diaglott when citing Philippians 2:8 in one place, but in the body text it consistently uses the word "stake" or "torture stake" when referring to the instrument of Jesus' execution.
As far as I know the cross has been replaced with the crux simplex to substantiate the fact that the cross, as a religious symbol, is of a pagan origin. Since most of the people believe that the cross as the symbol of Christendom was first chosen because of the fact that Jesus died on a cross, this was a pretty easy strategy to have a backing to their statement that Christendom is an apostate form of religion and to enforce future ex-Catholics to give up praying in front of a crucifix.
So, as it is the case with many of the changes, this too was made to help gather converts to the organization and to reach growing numbers more efficiently.