The problem with Barbarossa was that the further they got the more difficult fighting got, and thus the opposition has to lessen.
IOTL they had 4 aims. Destroy the red army, capture Leningrad (and unhinge the Soviet northern front), capture Moscow (and let the Soviet taste logistics problems) and take Ukraine (and improve long term strategic supply, and the oil is next).
IOTL they didn’t succeed anywhere, although partially in the south. Could they have avoided shuffling around panzer groups and achieved more? Most definitely. Certainly Leningrad was within reach freeing up more troops, with soviet surrenders, and a northern approach to Moscow with excellent supply lines.
For Moscow to fall here they have to avoid the Kiev encirclements which has negative butterflies, but the very positive one of wintering in Moscow with all weather airfields and soviet troop deployments in tatters.
Even if they are less advanced in the South this translates into a much better 1942.
The easiest is to somehow move forward or prevent the battle of Greece. Leaving aside the possible earlier start date, the armor deployed there was not available from the start of Barbarossa iotl, but should have been deployed in Romania. Had it been, encirclements would have taken place on this front as well taking away the need to be helped by AGC as well as possible butterflies in how fast the axis advance along the coast and take Odessa and this Sevastopol.
None of the above helps directly on the distance an AGS attack has to the oilfields, but it is a much stronger wehrmacht and likely weaker red Army facing off in 1942. Also, the bulk of the Army is here and on a single supply line outside Moscow meaning the Germans could deal a blow to the Soviets outside Moscow and move South-East to attack the caucasus now with waterways for transport all the way from Leningrad. Taking the East coast of the volga from that direction would leave the red Army poirly supplied and trapped in the Caucasus.
So imho there is a way. Basically stick to the plan in 1941 and the Germans might well in 2 years.