Instead of Black May, Glorious May

In May 1943, the Allies won the Battle of the Atlantic. Aided by codebreaking, huffduf and radar, their escorts and aircraft destroyed 37 German submarines (accidents raised the total loss to 41). The Germans had little to show for their sacrifices. Worldwide, in May 1943, they wrecked only 45 Allied merchantmen. In the North Atlantic, U-boats sank only 18 ships. Of the 450 merchant vessels in eastbound convoys (i.e. laden with cargoes for Britain) only 5--or about 1%--were sunk. No wonder the Germans called it "Black May."
Was the German disaster inevitable? Most historians would answer in the affirmative. I, however, suggest in May 1943 the Reich could've won a spectacular victory. And in the very place where defeat occurred--the critical North Atlantic run. The key to success was effective use of surface vessels as well as submarines.
It was unfortunate that the big ships of the Kriegsmarine had fallen out of favor by 1943. Scarcity of oil had idled Tirpitz, Scharnhorst and other large warships. Considering the vessels useless scrap iron, Hitler wanted to decomission them. The warships survived only because of their role in tying down British naval assets. They might, in fact, have accomplished much more.
As the May disaster showed, it was fallacious to think U-boats could carry on the sea war unassisted. Given stronger escort forces, they needed the help of the big ships. Tirpitz etc might've caused Allied convoys to scatter so U-boats could sink merchantmen without fear of escorts. That was achieved the previous July during the fight against convoy PQ17. The success might've been replicated in the Atlantic. The Germans, however, could've been even more ambitious. Consider this alternate scenario:

• First, in late April 1943, the Germans abandon the hunt for convoy ONs 5. Instead,  all available Type VII boats form a patrol line running south of Greenland (or perhaps two parallel north-south lines) with a 150km gap between the northernmost boat(s) and the Greenland ice sheet. Able to determine U-boat dispositions, the Allies route their convoys through this gap.
• In the stormy weather at the end of April, a German flotilla consisting of Tirpitz, Scharnhorst, Luetzow and a few other warships sorties from Norway, undetected by Allied aircraft, then grounded in bad weather. Maintaining radio silence, and sailing at low speed to conserve fuel, the flotilla heads for the Denmark strait. The allies are unaware that German ships pass through the Denmark strait and enter the Atlantic.
• Consisting of 46 ships, convoy HX 237 departs New York on May 1, and sets course for the Greenland gap, which it reaches around May 9. By then the German flotilla is deployed in the gap, waiting for it. Tirpitz and its companions surround the convoy and demand that all merchant crews abandon ship. Any ships that attempt to flee are hit a few times to stop them. To conserve ammunition, however, the warships usually don't sink them. They summon about 20 of the northernmost VIIs to finish off most of the stopped vessels. But the U-boats are ordered not to torpedo any tankers unless authorized. Tirpitz and others determine which tankers are carrying oil suitable for warships, put prize crews on them and sail away a certain distance to refuel from them. Except for a few escapees (mostly stragglers sailing behind the encircled, main body of ships), the rest of HX 237 is wiped out. Total allied losses to this point are 43 merchant ships (the convoy escorts fled).
• After the HX 237 disaster, the Allies halt further convoy sailings until they can either destroy the German ships or provide sufficient warship escorts. Convoy SC 128 had already passed through the gap before the flotilla arrived there, and SC 129 was routed through the new gap caused by the movement of 20 U-boats northward. After that, however, the Allies form a superconvoy, consisting of HX 238 (45 ships) HX 239 (42 ships) and SC 130 (37 ships), guarded by two battleships and five cruisers, plus the usual destroyer etc escort. The big convoy sails around May 20. By then the Germans, with many U-boats including several fresh from Kiel, have established a new patrol line without a gap, extending from Greenland to a point well to the south. To evade the U-boats, a convoy will have to pass south of the patrol line. 
• Anticipating that the allies would strengthen convoy defenses, the flotilla attempts to trick the escort into abandoning the big convoy. The Germans send a U-boat far to the south, to the Middle Atlantic area. The boat sends a message announcing that, due to mechanical problems, it can no longer escort one of the captured tankers, then in the area. To strengthen the ruse, the flotilla also sends a cruiser, low on ammunition, south where it can be spotted by a middle Atlantic convoy.
• By May 25, the Allied escort commander is ordered to detach his battleships and cruisers from the big convoy and send them south. With just the usual escort, the big convoy continues just south of the patrol line, around May 29. There the German flotilla pounces on it. By this point the allied warships have no hope of returning in time to repel the enemy. A huge convoy of 124 ships is surrounded and defenseless. Some escape, but most comply with the German demand to stop and abandon ship. U-boats again race to the scene to massacre merchantmen. Only a few tankers, as before, are temporarily spared. After two days of slaughter, allied losses amount to 112 merchant ships. In addition, on May 31, U-boats torpedo and sink a battleship, which was searching for the flotilla. Meanwhile, other vessels rescue survivors. Its ammunition spent, the flotilla dashes back up the Denmark strait and returns to Norway.

On the North Atlantic run alone, Allied losses in May 1943 are 155 merchantmen,  or about 950,000 tons--vastly surpassing that of any other month of the war. Released from anticonvoy duty, longer range Type IX U-boats bag another 250,000 tons, bringing the total for May to 1.2 million tons, an unprecedented haul. Given some intuition (notably realizing the allies could determine U-boat dispositions) careful planning and a bit of luck, the Germans could've snatched a spectacular victory from the jaws of defeat.