Are the Siberian troops really that important for Germany against Russia that they warrant screwing up the Japanese?
In my book, the Germans are camping in Smolensk in turn 6. Yes, because of the Siberian troops, you may not be able to take Moscow straightway, but the additional troops will only delay things for the Russians (this could matter if you attack the stack right away, but why do that?). In the game I played recently, the Japanese went through China to take Stalingrad and the Italians are breaking through the South also working with the Germans. The Germans are ready to flank the North side and continue with a light charge through Siberia (Japan has not activated the Mongolians). The Soviet Union is losing income fast and no longer has ability to counter-attack without risking their capital (the Siberian troops help defend, but not sufficiently for Russia to hold significantly more ground). So, it’s just a matter of time before Russia falls at that point. Marginal spending is needed on Germany, Italy and Japan’s part to squeeze the Russians into submission (say 25 IPCs for Germany, 9 IPC for Italy and 9 IPC for Japan).
Since only little spending is required to finish the job in Russia, Japan is able to keep the US (very strong but can’t be a lethal threat for a couple more turns and it can be handled), India and Anzac at bay (both are holding their ground, but weakened) and Italy / Germany are sufficiently strong to keep the UK and the US on the other side of the map.
The Germans / Italians / Japanese just need to hold their ground at that point (which costs a lot less than what the UK / US spends to go after them) while slowly squeezing the Russians from all sides. Think about what it costs to build a significant threat on the European side and the Japanese side.
1 transport + 1 infantry and 1 artillery = 14 IPC, if you let that Land, it takes only a few IPCs to deal with that. Transports require protection, which means many carriers + fighters. On the European side, these can be dealt with with a mix of submarines and planes much cheaper than what is required to protect the transports. So basically, build your airforce and Navy cannon fodder to make landings extremely costly. The allies can’t keep up with both building a significant landing force and deal with the fleet protecting that force. As the axis commander, you can decide to deal with the naval force (with air + sub fodder) OR the troops that landed with your air force (air + infantry fodder). That means that to keep up with you, the Allies need to spend almost three times as much 1) Naval defence, 2) transport capabilities, 3) ground troops. On your end, planes serve as 1) land defence, 2) land offense, 3) Naval offense. Only relatively modest amounts of subs / infantry are needed to complement that air force.
On Pacific, a combination of fighters / infantry on Japan is much cheaper defense than what the US needs to cause a lethal threat. A combination of planes / subs as a counterattack is much cheaper than defending against it. Japan can use land based planes to supplement their counterattacks. The US needs to hold zones / land which makes things a lot more difficult and costly.
In summary, I don’t think the Axis should be in a “hurry” to take Russia. You should reduce it and use logistical advantages (division of IPCs among Allied powers, need to build transports, protection force and the land force) to hold other fronts. If Russia is taken down and Axis are able to push back elsewhere, is there any way that Allies can win? If so what’s the hurry?