I assume the war would go the way it went because nothing you have said changes certain facts:
Fact 1: Nazi Germany and the USSR were natural enemies and a confrontation was inevitable.
Fact 2: Japan's atrocities in China had led to US sanctions, which in turn led to Japan's military response.
Fact 3: The USA was already preparing for war by 1940.
Fact 4: the mediterranean would have been no Barbarossa, because there's no way they could deploy even a small fraction of the Barbarossa forces in the Mediterranean.
Please review my first post in this thread, wherein I explained why it was already too late by 1940.
So whether it was 1941, or 1942, or 1943, the USSR and USA were coming into the war. Nothing Germany could do could change that. You falsely make neutrality equivalent to passivity. Neither the USSR nor the USA was being passive. Both were preparing for war. The USA was surprised by the Japanese attack, largely because we were preparing for war against Germany.
I think you, in turn, underestimate axis difficulties in the Mediterranean. Need I point out that historically, the advance into Egypt was halted, primarily due to the problems of supply. An army simply can't be supplied in north africa without shipping. The germans tried it, and failed. The british, who could supply their forces by sea succeeded. There would have been no reason to evacuate the british fleet before the germans reached the nile. How were they to cross the nile with no ships? The fact that you ignore these enormous logistical problems makes you hard to take seriously. I contend, Gibraltar or no Gibraltar, the Axis couldn't take Suez.
Unless...and this is the only big if-if these successes could bring Turkey into the war on the Axis side. Only then would taking Suez become possible. If Turkey were to join, troops and supplies could be moved by rail all the way to the middle East, and the whole thing easily accomplished. However, I bet that would have led to other consequences, like the end of the USSR sitting around and waiting to be attacked. And would Turkey have joined before the British Empire was defeated? I doubt it.
Also, I'd just like to briefly discuss the Malta vs Crete issue. It is true that in hindsight, squandering the german airborne forces on Crete rather than malta was a mistake. But why did they choose Crete to begin with? Let me tell you. Crete would have made the perfect place to bomb Romania from. Romania, the sole source of German oil. So trading Malta for Crete means allowing this bombing to take place. Just remember, everything you change has a cost to it, which I think you all too frequently ignore.
And finally, I am not overestimating the strength of the British Empire. Everything I have said has a strong basis in fact. The British navy was the most powerful in the world in 1940. The italian fleet never even dared leave port to challenge them. Facts. If you had managed to take Malta, all you would have gained was a narrow corridor to get shipping as far as Benghazi. After that, you have to truck everything across the desert. You think Russia is bad? You don't have to truck water in Russia. You couldn't send a bigger army to Africa, because you could never keep it supplied.
My contention that the British Empire could function even if divided in half is also well based on fact. The French, Dutch, and Belgian colonies in africa and indonesia continued to function after their home countries were completely occupied. India itself is a mighty nation and had a large industrial base even during that time.
To sum up, your plan involves invading another neutral country, and yet expecting the USA to remain neutral even longer than it did. Occupy another country, but fail to discount the number of troops necessary from your total avaiilable. For comparison, the occupation of Yugoslavia took more than 600,000 troops, and cost over 50,000 deaths to Germany and Italy, not even counting the minor axis contingents. Spain would have been just as costly. Then you surmise that this would allow the Axis to take Egypt, despite doing nothing to solve the Axis' own logistical problems, and ignoring the natural barriers to this advance, including that of one of the Earth's LARGEST RIVERS. You assume that the loss of Gibraltar would lead to the british fleet's withdrawl from the med, despite the fact that they had somewhere else to draw their supplies from (India via Suez). Indeed, you also ignore that Axis operations in the Eastern Med would be greatly hindered by Allied aircraft operating from Crete, which your plan leaves in their hands. The one factor that COULD actually have been a game changer, Turkey, you ignore.