Not to disagree with the majority of your post, but
3] New Caledonia, which as CalBear has described would be a monumental disaster. Fiji and Samoa, along with the New Hebrides and Ocean and Nauru Islands, were either lightly or completely undefended. But they were not the golden prize, as their relatively small size did not allow for the exploitation of major air bases.
Not to disagree with the majority of your post, but by the spring-summer of 1942, all of the larger island groups in the South Pacific were well-garrisoned by ground and air forces. As examples:
Samoas - Samoa Defense Force, which amounted to a light division of the USMC, built around the 2nd and 3rd Marine brigades (7th and 8th Marines) plus several Marine defense battalions, field and AA artillery, Marine and Navy engineers, etc.
Fiji - US 37th Infantry Division and NZ 3rd Division; total of five infantry brigade/regimental combat team equivalents, plus several Marine defense battalions, field and AA artillery, Marine and Navy engineers, etc.
New Caledonia (and the New Hebrides, etc) - The Americal Division (3 infantry RCTs), plus several coast, field , and AA artillery battalions, Army and Navy engineers, and two separate regiments, one of infantry and another of cavalry (actually still horsed, in fact)
The other smaller island chains worth bothering with (Societies, Tonga, etc) all had their own garrisons, ranging up to an infantry regiment in size; New Zealand itself had about six brigades of infantry and cavalry, while Australia was garrisoned by about seven divisions of AMF, two AIF infantry divisions (6th and 7th; the 9th was still in the Med), and two US army infantry divisions (32nd and 41st).
New Guinea's garrison was fairly slender early on (about two brigades of AMF) but was reinforced throughout the summer and autumn by more AMF brigades and the 6th and 7th AIF and 32nd and 41st US divisions.
Hawaii, in this period, was garrisoned by the RA 24th and 25th divisions (each with three full mainland RCTs), the remaining infantry regiment of the Hawaiian National Guard, the "square" 27th Division (four RCTs), various and sundry corps and army-level troops, coast and AA artillery, army and marine engineers, and 2-3 Marine defense battalions, plus the Hawaiian Defense Volunteers, some 20,000 milita organized at the company and battalion level as everything from infantry to cavalry to engineers to AA batteries. The 1st and 2nd Marine divisions were within a few days steaming, as well, of course.
The Japanese, at their strongest in December, never had more than about four divisions afloat simultaneously, and trying to assemble the requisite transports to match that effort in 1942 would have actually required reducing the flow of supplies and replacements to Burma and the garrisons froim Thailand across to the Central Pacific...
All in all, the Japanese reached their high water mark in April-May, 1942 - they weren't going any farther, in any significant way.
Best,