You’ll have to consider whether you can hold at least Cairo while much of the US forces would be away to deal with Japan. The problem is that if you don’t do anything about Japan, it will just keep growing. Hawaii and Sydney seem safe for now, but you’ll lose the economic game if you maintain the stalemate situation in Europe while ignoring Japan. In fact, if you were playing a good human player, you’d most likely lose this game for that reason. Against the AI it will take longer, but generally it does a decent job building land units and sending them towards the enemy. Which, in Japan’s case, will be Russia. So if you keep on doing what you’re doing now, Russia will fall.
It’s at sea where the AI’s main weakness lies, but Anzac alone can’t keep it in check. In fact, that Anzac fleet at the Carolines is counterproductive, because the AI will see the direct threat to Japan, and keep Japan defended against a force of that size. So if Anzac can afford it (I don’t know about the state of the Japanese navy), it would do better to start eating at Japanese possessions that are more remote (maybe the Dutch East Indies), and the AI will start shipping troops away from Japan to use them elsewhere. Once that happens, you can sail your US invasion fleet to Hawaii. But make sure you have enough to defeat anything they build (10 units) plus any planes they may land.
A naval base may help to quickly transfer your Atlantic fleet, but it’s better placed in Southeast Mexico if you want one in that region. And remember that when your transports are in SZ 101 (US east coast), they can reach Hawaii in two turns anyway.
On a side note, the AI will typically fall for the old Denmark trick (US takes Denmark, UK sails in to take a poorly protected Germany). And a UK plane on a US carrier may also do you some good in killing some unprotected transports.