After the three big ones, I first use ending letters, then name lengths: Tonga and Samoa, Fiji and Kiribati, Palau and Nauru, Vanuatu and Tuvalu (which are almost anagrams of each other), Marshall/Solomon Islands, with Micronesia the third big island group.
I do PNG Australia New Zealand (big 3) then I do Fiji Samoa Tonga (3 off to the side) then Tuvalu Vanuatu Nauru (3 that rhyme) followed by Marshall Islands and Solomon Islands (both names have islands) and lastly Kiribati FSM Palau (3 stretching east west) It might sound complicated but for me it works!
Nice quiz, but shouldn't the instructions say "most southerly in latitude" rather than "lowest in latitude"? "Lowest" means closest to zero, ie closest to the equator, like Singapore.
Starts With M: Marshall Islands, Micronesia
Starts With P: Palau, Papua New Guinea
Starts With S: Samoa, Solomon Islands
Starts With T: Tonga Tuvalu
Ends With I: Fiji Kiribati
Ends With U: Nauru Vanuatu
The Major 2: New Zealand and Australia
The first group is: Fiji, Tonga, Samoa
Second group is: Vanuatu, Tuvalu, Kiribati
Third group is: Marshall Islands, Solomon Islands, Micronesia
Fourth group is: Nauru, Palau
PNG is easy to remember