From: Jackson Tn
I also believe Russia at some point would have invaded Germany.
The problem was Germany wasn't ready to take on Russia in '41. They had squandered the Luftwaffe over Britain and needed time to replace loses from the previous campaigns, plus their tanks where not upto the mark to take on Russian tanks, maybe in '43 they'd have been far better prepared, however if Russia was building up for an attack in the near future they might not have had that amount of time.
I feel though if they had held off for a year or so and given Rommel more support instead in Africa and they managed to push up through Iraq\Iran things would have been different as they'd be close to their furthest point they got to in the attack against Russia with probably far fewer casualties. Russia would have been in a tricky position then from the West and South. The Germans may have brought Turkey into the War on their side aswell at that point. I'm sure Hitler was peeved with Japan for attacking the USA instead of helping him with Russia, as soon as they did that even in this scenario he would be in trouble no matter what.
I think you are correct that Russia would have invaded Germany. Hitler was only seeing want he wanted over the Japanese attack on America. He wanted to embarrass Roosevelt, in his speech declaring war on the U.S. Hitler said:
"National Socialism came to power in Germany in the same year as Roosevelt was elected President…While an unprecedented revival of economic life, culture and art took place in Germany under National Socialist leadership, President Roosevelt did not succeed in bringing about even the slightest improvement in his own country."
Hitler also thought, foolishly, that America would go after Japan first, diverting it's shipping to the Pacific. Apparently he thought this would make his war in Europe easier.
These things just give you a glimpse into Hitler's way of thinking, which is in indicative of how he thought of Russia.
Ah, a moment of glory for me to bask in...it's over though.
"I hate newspapermen. They come into camp and pick up their camp rumors and print them as facts. I regard them as spies, which, in truth, they are. If I killed them all there would be news from Hell before breakfast."- W.T. Sherman