As for getting the Caucuses early, it provides an excellent launching ground against Russia proper. If you can keep Caucuses, it most likely means Germany can mop up the rest of Russia and hopefully you have invested just enough to take most of Africa for the IPCs. This means Germany is loading up the cash and with that you can soften up Russia by launching small attacks every turn with tanks and a few infantry to soak up hits so ideally you are taking out basically what Russia is putting in there every turn given its low IPC count (btw, if Germany can take most of the western holdings in Russia, I would go with Japan all out against the rest of Russia as even the few IPCs it can capture can make the difference in the long run for Russian INF production which, as a purely defensive force, Russia is now most likely static with no spoiler attacks… they’re waiting to be saved by UK/ USA). I would probably go 4 tanks every turn in CAU but ONLY if you have the INF marching forward every turn from Germany proper to give you the fodder you need. You don’t want to set up a spoiler attack by what limited Russian forces might be left that could delay Germany just long enough to let the UK/ USA get in there.
Keep pouring the INF across to the east and eventually you should have enough fodder + tanks to launch the decisive attack on Moscow even if you are allocating a few INF every turn to West Europe. I would agree that it is optimal if somehow you can ensure that Japan is the actual one to capture Moscow as this will really help you out production wise, so if you can get it where Germany hits Russia hard and reduces them to rubble AND neither the UK nor USA can reinforce enough, try and take Moscow with Japanese forces.