I agree with you that if Yamamoto is smart he will fortify the key islands.
Also I agree that Yamamoto was looking to keep up the offensive. Yamamoto was intelligent as well as a gambler. He would not have ignored fortifying the islands at the cost of offensive operations. The FS Operation was postponed then cancelled because of the battles of Coral Sea and Midway. But it is possible that if Midway was the disaster we are hypothesizing here that Yamamoto might actually see seizing New Caledonia, Fiji, and Samoa as the perfect way to try and cut off American troops and supplies reaching Australia.
He might actually succeed too. I think it would be pushing Japanese supply lines to their absolute limit but if Yamamoto moved fast enough-i.e. within the six month window bought by the Midway battle he might, I emphasize might be able to pull it off.
However conversely, would the USN risk its two or at this point three carriers to try and stop him? I think so. I think you might have your decisive battle in the vicinity around the targets of Operation FS.
1. The IJN could take, perhaps, Espiritu Santu. But beyond that? Even Efate had a sizable garrison that included an entire Marine Defense Battalion by late May. And as I noted above, by spring New Caledonia had over 22,000 regular troops, featuring almost the entire Americal Division (arguably the best trained US Army infantry division in the world at that time), with another 13,000 added by end of summer. It was superbly defensible due to terrain and nearly continuous coral reefs. It would have been a multi-division operation (requiring several weeks to months to secure) for the Japanese, almost on the scale of the Philippines - only this time on virtually the other side of the world, rather than just 300km from Formosa. Fiji would have been almost as bad. Remember: The Japanese in OTL couldn't even evict a single under-equipped Marine Division from Guadalcanal, even with multiple windows of isolation from U.S. naval protection!
I submit that anything beyond Espiritu Santu is simply beyond Japanese capabilities, and they would have quickly discovered this the hard way had they tried. They did not have the shipping, the available troops, the logistics, or the air support - not at that point in time. IJN intelligence simply had no idea how heavily defended these major islands were by the spring of 1942, let alone by the end of summer. If they had, Operation FS would have been deep-sixed.
You can read a lot more about U.S. efforts to build up these islands in 1942
here.
Port Moresby really is, I think, the one credible option for them.
2.
Saratoga and
Wasp - which is all Nimitz would have in July, assuming he loses all three carriers at Midway - is not a match for the full Kido Butai, assuming Yamamoto waits until early August when
Shokaku and
Zuikaku were available. But they would have nearly half the air complement of the KB, enough to play a spoiler role on the flank in cooperation with land-based air assets in the New Hebrides and Queensland, perhaps waiting until Nagumo's air groups had been chewed down establishing air supremacy over New Cal. (It's probably safe to assume
Ranger could not reach the South Pacific until September.) If FS is delayed until then, however, Halsey starts to have a fairly formidable force.
3. As others have noted earlier in the thread, Nimitz was hand-picked by FDR, leaping over dozens of more senior admirals. It's really hard to see him sacking Nimitz losing a battle against a superior Japanese force, especially after he'd played for a draw at Coral Sea. Fletcher and Spruance, on the other hand, might see the end of their useful employment, if they survive the battle (which would be a pity, as both were fine commanders).