Is there a way to save the Russkies? If you drop the Japs instead, take the South Pacific Theater out of the equation, then you could make this a Fortress Europa-themed conflict. Russia really was allied with Germany early on, so clouded alliances between Western Axis and Allied powers would be believable.
Here's a twist: In his book "Currahee!: A Screaming Eagle at Normandy", Donald Burgett claims to have seen a dead Japanese officer in Normandy. The writer of the introduction thinks he probably saw a dead Russian with Mongol features (a large part of Russia is in Asia, after all). But what if, in our scenario, there actually WERE Japanese soldiers fighting in Europe? If a small Japanese force were attached to the German army, then the Japanese general could command the Germans/Japs, freeing Rome to go back to commanding Russia. There would still be four armies, but people who wanted to be Japanese could still be. The combined army would then have split special powers, but only those playing as Germans could use the German power, and those playing as Japs could use the Japanese power.
Probably too confusing, but I'm just thinkin' out loud.
---Lee