A relative of the papaya/paw-paw is the babaco, Carica x pentagona (syn. Vasconcellea × heilbornii), a wild hybrid from the Andes foothills in Ecuador. It seems to be slightly more cold-tolerant than the papaya itself, fruiting readily in less tropical conditions. We saw this one fruiting well in David Glenn's experimental tropical-fruit garden at Heronswood, near Melbourne, during the MGS visit to Victoria and South Australia last October. David's climate is more or less mediterranean, and he said his "tree" (like papayas, they're really overgrown herbaceous plants) had been perfectly happy in both hot dry summers and slight frosts.
He said that the flavour was broadly similar to papaya (which he hasn't been able to grow to fruit so well), though less musky and perhaps rather blander.
Has anyone tried this? Like the papaya, it's very quick to fruit from seed - in ideal conditions, within a year.