Roosevelt wasn't that Machiavellian, Stalin's view was always fueled by paranoia. FDR misunderstood Stalin, calling him "Uncle Joe." FDR thought he could work with Stalin. Churchill understood what was happening in the East, his call for invading the Balkans and Norway instead of Normandy was to get western Allied troops as far east as possible to prevent the Soviets from getting into Eastern Europe. Churchill was listening to people like the Poles who were already complaining in 1944 that Soviet occupation was little better for them than the Nazis.
Intriguing point about the Soviets accepting a separate peace if the Normandy invasion failed. I'm not so sure the Russians would have given up though. They suffered too much. It's all speculation of course, but I believe the biggest implication of a failed Normandy invasion likely would have meant much of Western Europe would have ended up under Soviet domination.
In any event, the war in Europe ends in August of 1945 when the US is capable of deploying the atomic bomb. If Normandy fails, could the Soviets have taken Berlin by May 1945? If the Germans can shift divisions from west to east maybe they are still in Russia when the atomic bombs drop. One wonders how that would have affected the outcome of the war. Hitler would never surrender but if Berlin were nuked and Hitler were dead, maybe Germans like Donitz form a new government, make a separate peace and the Reich continues in some form. Maybe things return to 1939 borders. Maybe the Soviets can't get as much of Eastern Europe. Europe/the world would have been a much different place with an independent German power, the Soviet Union and a US and Britain that had not beaten the Germans on the battlefield. Once again, it's all pure speculation but there's no right or wrong answer since it's all hypothetical.