This is an interesting question. Assuming Germany makes peace with a Russian rump state and the border is along the AA line, then Germany has the oil of the Caucuses and the Black Sea is now secure. This largely fixes Germany's oil problems. It even opens the possibility of a strike from the Caucuses towards Iran and Iraq. However, I think in this scenario the British and American control of the seas means an allied build up in Iran (Persia) and Ploesti style B-17 and B-24 raids on Baku and other oil sites. Later on B-29s join in.
Axis logistics in the Mediterranean will still be iffy even if there is no local opposition. The allies should be able to pull off operation Torch, but taking Sicily or Sardinia would be exceedingly difficult. An unbroken/unengaged vs. Russia Luftwaffe would make it quite dangerous to operate naval units in the Med, and the American carriers are still needed to fight Japan. I'm thinking it would be necessary to build up large air bases in Algeria, Tunisia, etc. to at least stalemate the Luftwaffe before a Sicily invasion could take place.
The big question then is, what next? I can see B-36s bombing Germany, ME-262's struggling to get high enough to intercept them. Slip in a few atomic bombs and maybe Germany surrenders. The big question is, could a D-Day overlord invasion succeed against an intact German army with 15 Panzer divisions and an intact Luftwaffe? Pretty iffy proposition in my opinion. Will atomic strikes on Berlin, Hamburg, etc. be enough? Not sure.