I considered it too, but agree with the others: do not try it. Japan is better letting US come after it once it has made its gains and money in Asia. Hawaii leaves you on the wrong side of the pacific, with your best asset, the fleet, stretched and liable to destruction.
Japan is better off never facing the US Navy in the Pacific. With that said, you can get your fleet a significant head start on its way to Calcutta and if you decide the odds aren’t in your favor, just keep moving towards Egypt.
It pairs real well with a German move towards Moscow, shortening the game that the Allies get to play for in Europe.
As for DoW, J2 or J3 seems to make more sense as you aren’t focused on winning in the Pacific, but getting your fleet around to Calcutta and either taking it or skipping it to land your TT convoy in Iraq. The US has a hard time taking Japan if from J3 onward you just invest IPC in defending your capital and getting Bombers out of Japan, into China and then either hitting Calcutta or skipping across it.
I’ve had 7 TT with Inf/Art land in Egypt and staged for Egypt on the next round. The 1-2 Punch of Italy and Japan pretty much assures Egypt is in Axis hands right around the time Germany should be planning on taking Moscow which = GG for the Allies.
I personally prefer this route over anything else and India is helpless to stop your fleet from skipping right past it once it goes into Inf Defensive mode with the obvious feign to take Calcutta. The US is way too far behind to catch up even its initial early purchases if you keep yourself along the coastline of the South Pacific with your Navy.
At worst, the US convoys Japan for 8 IPC for that 52+ IPC it spent trying to kill your navy early on, but Japan isn’t there to win an economic battle in this move, but in it to assist Italy in easily taking and holding Egypt before the Allies can realistically get themselves into the Med to even try to reclaim it (let along address the full Japanese Navy that likely lost zero to no ships from the start).