Although New Guinea may be part of Melanesia, Melanesia refers to the region of Oceania that includes the countries of Fiji, Solomon Islands, Vanuatu, Nauru and Papua New Guinea, as well as the regions of Papua, West Papua and New Caledonia. Melanesia does not, however, refer to the Malay archipelago, despite their sharing of New Guinea.
Please consider what to do with Leeward and Windward Islands. It's hard to tell where one archipelago ends and another begins, so this division of the Lesser Antilles is a reasonable answer.
I believe the Quizmaster has an external source to which he gets the official Jetpunk maps. I'm all for adding more islands, but the Polar islands such as Svalbard have to be flattened greatly.