(Part 2 -- continuing from my immediately previous comment)
It can be assumed that Hitler's indecisive delays and arguments were unnecessary.
But the Russians had very strong forces in the Ukraine (massed there prior to the German invasion of the Soviet Union on June 22 (Barbarossa), apparently with plans to invade Romania, according to interrogation of Soviet prisoners by the Germans). In any case, it was important to neutralize these forces to prevent them from interfering with the sdvance of Army Group Center as it drove to Moscow. It must therefore be proven that the additional month's delay while Guderian was diverted to help Army Group Center in the Ukraine on August 25, was also unnecessary.
Army Group South faced numerically superior forces, but despite interference from Hitler which turned a planned double encirclement into a frontal attack, by July 7 Army Group South had " equal strength due to heavy losses inflicted on the enemy and soon would add numerical superiority to tactical and operational superiority" (Generaloberst Franz Halder's diary for July 7 as quoted by Stolfi); and in fact by August 1 Army Group South estimated it had forty-one German infantry divisions versus twenty-nine Soviet rifle divisions (ibid. for August 1).
Well before the August 25 diversion of Guderian to the Ukraine, Army Group South had "pinned down - indeed severely mauled - Soviet forces in the Ukraine. Army Group Center therefore retained complete operational freedom of movement to advance on Moscow, limited only by its own immediate problems of reorganization, rest, and resupply" (Stolfi).
I will leave Stolfi's logistical demonstrations of the plausibility of the latter to readers of his detailed and well-sourced book.
Suffice it to say that he posits a hypothetical advance on Moscow beginning August 13, instead of the historical September 30, 1941; capturing the capital on August 31, taking six days to clean up pockets of Soviets around Moscow, followed by "five days of reorganization, rest, and maintenance of equipment in Moscow, in a great arc around it". He also posits the establishment of winter defensive positions along sections of the Volga by October 10. So in fact there is some leeway in his timetable.
Since the Soviet defense of Leningrad and the Ukraine depended on Soviet control of the rail hub and vast marshalling and storage facilities of Moscow, seizure of Moscow at the end of August would strategically isolate the Soviet field armies west of Moscow from the remainder of the state and force them to withdraw or be destroyed. I should also point out that toward the German goal of the prevention of the escape of these forces, Stolfi posits encircling actions and cauldron battles, similar to those previously carried out with great success by the Germans, by Army Groups North, Center, and South, prior to retiring to winter lines by October 10.
Quite aside from the advantages of seizing Moscow's rail hub, storage centers, and communications network, as well as winter clothing and lubricants (though the Germans would have indoor shelter in Moscow and cities like Gorki on the Volga, and would also have time to bring up supplies themselves), there is the fact that the Soviets would have lost the vast armaments (and other) factories of Moscow and Tula, including the T-34 factories, the breadbasket of the Ukraine, and in general the industrial output of European Russia. By contrast, the Germans would have gained vast mineral and fuel and other resources, including equipment left behind by or captured from, the Soviets.
Then there is the matter of the capture or destruction of the Soviet government, based in Moscow. It might be destroyed, in which case the snake has lost its head (though a hydra might grow another one); ot it might flee across the Volga in a panic as German forces close in. Zhukov wrote that on October 17 the Soviet General Staff and Supreme Headquarters were divided in two, and Reserve Headquarters was set up in the East, in case Moscow fell; but in the hypothetical, Moscow falls by the start of September.
Still, the Soviet Union would remain a vast place with vast resources, including not only the reserves still unbeaten in the Far East, but also manufacturing centers established in the Urals as previously retreating populations moved whole factories lock, stock and barrel. The Far East reserves consist of 30 divisions, many tanks, and 2,800 warplanes.
Here, Stolfi simply waves his hands and assumes inevitable German victory.
But there are several possibilities. With the Soviet Union a ruined rump state in the East, its government in hiding, disconnected, ill-informed, or perhaps even gone, and this by August 31, the Japanese might reconsider their intentions in the Far East. Pearl Harbor did not occur until December 7, more than three months later. How can the Russians transfer reserves preventing an attack from that side that they were expecting all along? Stalin didn't receive his report from Serge until October 5, but by that time the Japanese would in this hypothetical be well aware of the seizure of Moscow at the end of August, and might make other plans.
As for the armaments and other factories in the Urals, even in mid-1943 60 percent of essential optical parts and electronics was still manufactured in Moscow. But as Albert Speer points out, "the destruction of a few large power plants in the Urals would have put a halt to much of Soviet steel production as well as to tank and munitions manufacture. A direct hit on the turbines or their conduits would have released masses of water of a destructiveness greater than that of many bombs. Since many of the major Soviet power plants had been built with the assistance of German companies, we were able to obtain very good data on them".
From Gorki on the Volga, the Germans would be only 442 airmiles from the Urals, by my estimation: in range not only to Ju-88 and other bombers, but also to long-range escort fighters like the Messerschmitt Bf 110G/R3, with a range of 1,305 miles and a flight ceiling of 26,000 feet. And if it proved necessary or desirable, the Germans could use or build even more forward airbases.
Even if the Japanese went through with their Pearl Harbor attack, all Hitler has to do is avoid the elementary error of declaring war on the United States, in order to remain master of Europe while the Americans are busy with a Pacific war. The British, particularly if treated generously by the Germans, might well accept a negotiated peace settlement.