Survival of Nazi Germany
Basically, to get Nazi Germany to survive, we want to keep it from biting off more than it can chew. Keep it from being defeated, but don’t give Hitler too much success or any very long term conflict. We won’t mess with things too seriously - have the war start as normally. But we want to stop the war with Britain (because eventually Britain might inconvenience us by winning, especially by dragging the US into it), and we want to keep Hitler from attacking Russia. Aside from giving him an uncharacteristic infusion of sense, the best way seems to be to make the war go worse for him than it actually did, so that he won’t be able to invade. It might go something like this...
First step is Norway. The British get the drop on this one, as could easily happen if they got their act together a bit or the Germans were delayed. We’re talking a matter of a few days lead compared to OTL for the British, resulting in their gaining a foothold and using the Royal Navy to block any serious German invasion attempt. This is an important first step, a clear sign that Germany can be defeated, and a clear success for the British administration.
Soon after, the Germans invade France - but in this timeline their plans were not captured by the Dutch, and they stick to the original axis of attack through the Low Countries. Unlike their thrust through the Ardennes in our own history, this attack meets one of the main bodies of Allied defenders, significantly slowing down the early stages of the campaign. The Germans manage to recover, and the military effects in the short term are not severe. The invasion is, however, several weeks behind its OTL schedule, giving the Allies time to reinforce and increasing French resolve. In this timeline, the Germans seize Paris in July of 1940, but significant Allied resistance continues even after this. There is no Dunkirk-style encirclement, and the BEF continues to fight on in its entirety. It is September of 1940 before the French government finally surrenders, with more than half the country overrun by the German army. The British, and substantial French forces opposed to the surrender, withdraw from ports in southern and western France. The Free French government in exile sets up its headquarters in North Africa.
This has accomplished two things. First, Germany has suffered much more damage to its armed forces, and will thus take that much more time to recover to full offensive strength (Barbarossa in 1941 is now an impossibility). Second, Britain has held out much more effectively and even won an important victory under the old government, keeping the appeasers from being as thoroughly discredited as they were in our own history. The improved British position, and the longer French holdout, will also affect the war in the Mediterranean, though I am not sure to what extent. Il Duce may be given pause by the rather longer battle for France, which his army is participating in. It looks plausible that the Italian incursions into Africa, if they happen at all, can be defeated before the Germans gain any significant foothold there. Preventing a significant battle in Africa is important, because it means that by 1941, Britain and Germany are not engaged in direct land warfare, only the indecisive conflicts in the air and at sea.
1941 is the great year of stalemate. Britain and Germany are engaged in air warfare, with a slight advantage to the British but no decisive action. The Kreigsmarine has been destroyed, but the U-boats still keep the Battle of the Atlantic running in high gear. During the winter the British blocked off most iron ore shipments to Germany, slowing Hitler’s military plans even further. The only real accomplishment of Nazi Germany in the whole of 1941 is cementing of its control over Eastern Europe. The British, on the other hand, have established their positions in Norway and North Africa, and with financial assistance from the US are building up their forces for an attack on the “soft underbelly of Europe”. Russia has fully fortified its conquests, and reorganized the Red Army following the Finnish debacle. The situation does not look good for Germany - although Hitler does not realize it yet, he can no longer defeat either Britain or Russia, let alone both. At this point, peace feelers are sent out by both sides, but initially neither is serious enough to compromise much and it doesn’t get anywhere. Later in the year, it is Hitler who begins to panic. He has never really wanted war with Britain, something he now believes more fervently than ever since his western attack met with such qualified success. Stalin is growing visibly stronger and Germany is frittering away its strength in air and naval battles against Britain that seem to be going nowhere.
After a discussion with his generals, who are cautiously optimistic about being able to hold off Britain but wildly opposed to any attack on Russia, Hitler realizes he must be willing to back down in the west to realize his dream of Lebensraum, both in military terms and in terms of overriding internal opposition. It is the Germans who make the initial concession that leads to the opening of true negotiations - if Britain will agree to peace, Germany will begin a staged withdrawal from the conquered Western territories.
In November of 1941, a treaty of armistice is signed between Britain and Nazi Germany. Britain agrees to withdraw from Norway, secretly agrees to noninterference in any German efforts toward the “containment of Communism”, and declares its intent not to contest German borders. Germany begins a staged withdrawal from France, the Low Countries, and Denmark, and agrees not to support any power acting in opposition to Britain or its allies. Various other similar provisions and assurances are made, but essentially, Germany withdraws from all conquests except Poland. The British will have to have a stronger peace faction than they did at this point in our own history, as a Britain unified under Churchill would likely not agree. In this timeline, since it is clear that Germany cannot threaten Britain or its possessions, they are likely to accept a significant reduction in German occupation in order to avoid bankrupting the Empire, which they would have to do in order to defeat Germany alone.
So we get Germany and Britain at peace, with Europe subdued and demilitarized for the time being, but soon not under German Control. The Greater German Reich still dominates Europe, although it is in for some rough time. Now we get 1942. Stalin, ever paranoid, has realized that Germany is free to attack him and grows more prepared every day. The false words of friendship between Russia and Germany are now largely ended, as Stalin has reached a position of strength and wishes to present it to the Nazis, who he believes will attack at any sign of weakness. Germany is beginning to have internal troubles - torn between rearming to take on Russia, the problems of withdrawal from the occupied territories and setting up new defensive frontiers, and pressure to focus more on civilian production, the German economy is showing serious signs of strain. There are continued tensions with the Allies over the implementation of withdrawals.
At this point, all we need is to keep Germany from attacking Russia, and to keep it reasonably competitive as a third power (harder than it sounds in the long term, though the Reich has a greater population base than OTL’s Germany, but it can maintain satellite states in Eastern Europe). Keeping it from attacking Russia can be accomplished by giving Germany enough internal turmoil for 5-10 years (until the atomic bomb gets invented) to keep it from being overly aggressive. It shouldn’t be hard to bring this about - Germany is facing economic problems, serious unpopularity with the rest of the world, threats to Hitler’s leadership, and quite possibly beginning this timeline’s Holocaust. It shouldn’t be difficult to get Hitler into an inward-looking campaign of “purifying the Reich” in preparation for a long-term conflict against Russia. Kill the Jews, purge the anti-Nazis in the military, give Speer a free hand to bring the new territories into productive membership in the German economy, or whatever. All that nasty totalitarian stuff that makes for good stories, and as a bonus, it could be refreshingly different from all that other nasty totalitarian stuff the Nazis did.
Long-term, how powerful Nazi Germany would be depends on its internal situation. I haven’t looked up the population figures, but the Greater German Reich probably has approximately half the population that the US and USSR do, with a per-capita economy in between them, and initially a technological base that is competitive with the leading democracies. If it manages to recover from the inevitable economic turmoil and internal disturbances resulting from the failure of its large-scale offensive efforts, then it is certainly superpower material, although it’s probably going to be less powerful than the USSR, let alone the US.
The economic policies of “National Socialism” combine small-scale enterprise with government-supported corporate cronyism. While inefficient, even under economic direction such as Speer’s ministry, it is more efficient than Soviet communism. Combined with the head start of the more advanced German state, the Nazis can be serious competition in economic and technological terms to the USSR, although they may not be quite as effective as it in either category (the Soviets are, after all, twice as big and with considerably more resources). Needless to say, if the Reich is a sort of smaller, somewhat less powerful USSR, it’s got the same problems when facing the US and other western powers that the Soviets did. Can’t compete economically, can only compete scientifically in a limited number of areas, and can only compete militarily with very high levels of spending. I don’t think the Nazis could or would maintain the proportional military budgets the USSR did without experiencing even more severe military problems, so they’re probably militarily weaker, and thus will have to focus most of their forces on defending against the Soviet threat.
Strategically, if this three way cold war was expressed as a three-legged stool, you’d as likely slide off it as sit on it due to the unevenness. The Soviets are likely even tougher than in our own timeline, due to not being devastated in WW2. The West suffers the loss of several countries which were strategically and economically important, but not major military contributors, and Britain likely remains rather more influential. It is less powerful, but not substantially so. Germany may be powerful enough to compete with either on a semi-equal basis in terms of military force, but its strategic position is much worse. It is caught directly between the USSR to the east, and the Allied front line nations in the West. It must face both at once, whereas no major Allied nations are vulnerable to conventional Soviet attack. All in all, I think the scenario is interesting and I invite ideas on how it might plausibly be developed.