Taking any Allied islands should be considered a luxury move. Do it after critical territories are secured.
Not quite. The question of whether to attack Australia depends on what the Russians did in round 1. IF Russia is making a strong Asian stand (ie: if the Russian fighter was sent on the Manchurian attack and/or if 2 or more Russian INF were sent east in round 1) then I would agree with you: Pull all Japan forces back to Japan proper, assault Manchuria with so much overwhelming force that Russia is basically totally defeated in the east, then move toward Moscow as described elsewhere.
However, if Russia did not attack Manchuria at all, or if their attack forces were not at maximum strength, or if Russia sent all available forces west to defend Karelia, then you do not have to send EVERYTHING against Russia. In fact, “wasting” both battleships sitting in home waters is counter-productive to Japan’s openning strength: navy.
Remember, the US has to stage forward to attack Japan, or any navy around Japan. That means that Western US navy has to move to Hawaii (or Midway, or Wake, or SOMEWHERE forward of California) one round before it can attack Japan’s home waters (and that transport fleet you started building in round 1). Japan has more than enough initial air power to counter any Round 1 US attack, and then you simply re-start building that transport fleet and move the Australian navy back toward home waters. And if the US does stage forward, then the TWO Japan fleets pincer it, destroy it, and then keep building their transports to attack Russia and threaten Midway, Hawaii, and Alaska.