I would say the crop package is actually a overblown itself, on the condition that the theoretical colonizer had access to long distance trade routes. The Cholas, various Indonesian empires or the Malians, for instance all had trade networks with temperate areas: The Cholas and Indonesian maritime empires like Srivijaya regularly traded with cooler areas, like North India or China via sea, while the Malians had the gold-salt trade that linked them with the rest of Dar-Al-Islam, and its temperate crops and agricultural technologies. So, colonizing temperate Australia or even the Pacific coast of the Americas for the former two would be no big deal: Just as the Polynesians brought useful
canoe plants with them, the Cholas or the Srivijayans could easily bring temperate plants in their ocean-going ships.
Even just trade with or access to temperate-like mountains in the tropics, including at home, such as New Guinea Highlands, for a much more extensive
ATL* "
Trans-New Guinean Expansion, preceding and taking the place of, and perhaps being even more extensive than, the Austronesian Expansion, could enable easy colonization of New Zealand and South Australia, or further still.
Finally, even continental expansion could lead to colonization of temperate areas by tropical peoples, such as if the Inka Empire expanded further into the Southern Cone: Potatoes, Andean lupins, llamas, alpacas and quinoa, amongst other highland crops, do quite perfectly fine there in OTL, so the same could be expected for an ATL eastward Inka Expansion into the Pampas, for example.
*Note: The ATL I linked to is NOT mine
