Denkt, here's an alternative, if useless and impractical, but perhaps more historical suggestion.
I think firstly that almost certainly the Soviets should be handled in exactly the same way as the other Dictatorships are, Comrade Stalin makes all the decisions, woe betide anyone who screws up or refuses (the turn over for Soviet generals could be rather high, though it'd be no fun for people playing). That said, Stalin isn't quite as incompetent as Hitler and as the war progressed, Stalin gave more and more freedom to his generals, who rewarded him with victories, whilst Hitler went the opposite way, with him taking more and more power for himself as the fighting went on and deteriorated for the Germans, exacerbating the problems they faced.
(obviously with 20/20 hindsight, the fuhrerbunker won't be quite so deranged as it was, even through roleplay, I hope...

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The way Soviet high command (or as they called it, the Stavka) was that they controlled basically everything (pretty simple) and issued directives etc, however, when there was a vital operation or defence taking place, then they'd send a Stavka representative with full powers to do whatever was neccessary (iirc) to restore the situation or else plan it to a successful conclusion. A good example of this was the early stages of the siege of Leningrad where Zhukov was sent in to restore the situation there.
The way I see a semi realistic Soviet Union working is that the various armies and fronts will all be under ai control and when a really crucial situation arises then a Stavka representative (one of us) goes in and handles everything division by division (because it's simply impossible to keep everything under control on the eastern front).
Also, there were a ton of Fronts and Armies, especially toward the end of the way, I'm imagining it so that 3 guys have command of say the Northern Front, Western (Central) Front and Southern Front, roughly similar to Army groups A, B and C for Operation Barbarossa on the German side. Then you'd have one guy at Stavka handling where everything (replacements etc) are sent and then comrade Stalin in charge.
It's not unrealistic to have Stalin handling technology as well, as well as production. He spends the war working ridiculous hours (like all the leaders) fuelled on alcohol and you find his scribble on everything related to production and technology. He famously wrote : "the Il-2 is as important to the Red Army as Bread and Air" in response to factories not reaching their production quotas. That said, the top guy might find himself overworked if that's the case. Depends how we go. Maybe we need to start preparing to fuel him on alcohol too.
No idea how to work this, but particularly later on in the war, Stalin went out of his way to promote competition between generals, though might make for a less than enjoyable experience for us players.
Sorry, this is hardly even a suggestion, but here's how it sort of worked in reality.
I also have a feeling that the Airforce was subordinated to the Red Army... but I can't confirm...