Hitler's primary problem was that he bit off far more than he could chew just on the continent. His first policy should have been to leave Russia the heck alone. Save that adventure for another lifetime, even, and consolidate the hold on Western Europe and North Africa.
If you're Hitler in that scenario, you first sign a cease-fire with Britain to buy time, while your cargo ships and tankers do a brisk business back and forth through the Mediterranean. Use the time to build ships in Oslo and Naples, and to build up heavy industry in Aleppo and Tripoli. Meanwhile your propaganda machine is running 24/7 to paint you as a benevolent strongman who has brought order, intellectual rigor, and ethical purity to the mishmash of decadent cultures formerly known as Continental Europe.
Meanwhile, you're massing troops and materiel just north of Paris, including a new generation of ocean-capable amphibious landing craft. Regular sorties of Me-109s on the French shoreline keep the Brits from flying over to get a look at what you're doing. An arrangement with Josef Stalin enables you to trade shipping rights through the Med for generous quantities of Russian coal and petroleum.
Switzerland, while still sovereign, is landlocked and dependent on its good business relationship with you in order to obtain necessary goods. They do your banking for you, and you allow them bread and paint and clothespins. Neither you nor the Swiss mind so much, because you're making each other rich. You pay for their services with the excellent diamonds that you've got coming out of Africa.
Five years after the signing of your cease-fire with Britain, you arrange a naval exercise in the North Atlantic using most of those big warships you've been building out of Oslo. While the Brits are looking the other way, you send a flight of very high-flying Junkers (the ones with the turbocharged piston diesels) with three of your newest toys (nukes) and you smear London into a smoking grease spot, preferably while Parliament is in session.
With no Prime Minister, no royalty, and no Lords to speak of, the island nation is relatively simple to occupy through amphibious assault. Meanwhile, the U.S. has been terribly busy dealing with the Japanese in the Pacific, and haven't got into the war in Europe because you'd signed a cease-fire with the Brits. And now it's too late for the Yanks to intervene to save England, because you now own it.
So if the U.S. wants to attempt a European adventure at this point, they've got to start by establishing a beachhead somewhere all by themselves, halfway around the world, and nearly half the U.S. population likes you because you've got good press. There's a senator from Missouri who likes to make a stink, but the New York Times paints that Truman fellow to be an ignorant, uncultured hayseed (as opposed to you, that lover of fine cuisine and the arts). Besides, you've got those nukes. There's a lot of bluster, but the U.S. never intervenes to save Britain.
More time goes by, and you cultivate your relationship with Mexico. (By now, you can probably write the ending yourself...) The important thing is, take your time. Don't plan on rolling the Panzer divisions into Texas until 1958, at least. In fact, it's probably better to never invade at all. Do your best to split up the third world between yourself, Stalin, and Hirohito. Now that you've got the nukes, you can take Japan at your leisure. Do your best to own everything around the US and Canada, and let those countries isolate themselves. In fact, encourage them to do it. Maintain as cordial a relationship as you can.
Meanwhile, you own everything else. When you think of it, close down the Med and the Baltic to Russian shipping, line the Polish border with heavy artillery, and let Stalin freeze in his godforsaken Moscow. Meanwhile, you're on the Riviera with your feet up, sipping Reisling and listening to Wagner.
Good press? After you just nuked London, that would be a stretch.