I always assumed that the idiomatic phrase home free had its origin in baseball, and at least one relevant dictionary seems to confirm this.
Christine Ammer, The American Heritage Dictionary of Idioms, Houghton Mifflin 1997 (online) home free In a secure or comfortable position, especially because of being certain to succeed [...] This expression probably alludes to safely reaching baseball's home plate, meaning one has scored a run. [Mid-1900s]
But a different dictionary suggests the idiom is used in both America and Australia, which is easily confirmed by examples from Australian publications (emphasis in examples is mine):
Cambridge International Dictionary of Idioms, Cambridge University Press 1998 (online)
be home free American & Australian to be certain to succeed at something because you have finished the most difficult part of it [...]
Australian Broadcasting Corporation: "The servile, unquestioning friendship with George Bush, which dragged our government into Iraq and saw it defend Guantanamo Bay, is just another distant chapter in our feted alliance history. The Australian government lawyers who said it was legal are also home free."
Sydney Morning Herald: "Another round of Senate estimates questions next week and the week after a new AFP brief to the DPP on possible criminal charges means Reith is still not home free."
Given that baseball is, in my understanding, a little-known sport in Australia, this appears to call into question the assumption that home free originated with this sport. What is the best available information we have about the origin of the phrase?