What about one where the chancellor of WWI Imperial Germany, Theobald Bethmann-Hollweg, doesn't oppose unrestricted submarine warfare in 1915, two years earlier than OTL beginning in 1917? With unrestricted sub warfare, Germany could dominate Allied shipping. America would enter the war, but keep most of its men in Mexico looking for Pancho Villa, and the great convoys of 1918 wouldn't appear. England took two years in OTL to make enough hydrophones and depth charges to find and destroy U-boats, and unrestricted sub attacks would make that number skyrocket. Eventually, Germany could force a victory on the Western Front with no need for Falkenhayn's desperate attack on Verdun. A Germany fighting a depleted Britain and France might be able to finally reach Paris in an offensive similar to Ludendorff's of 1918, only there would be no American Marines to oppose it. Ultimately, the unrestricted sub warfare would annihilate British will to fight and force them into an unfavorable treaty with France and Russia out of the fight.
This same strategy was posited by Sir Arthur Conan Doyle in his novel Danger of 1913, where he proposed a war between Britain and a fictional European state named Nordland. Nordland is on the verge of losing when the naval officer John Serious proposes using their 8 submarines to the Nordic King, who replies, "Ah, you would attack the English battleships with submarines?" Serious' reply: "Sire, I would never go near and English battleship." He outlines a proposal to attack all seaborne foodstuffs: "What do I care for the three-mile limit, or international law?" Needless to say, England is forced into a humiliating peace
If Bethmann-Hollweg is removed in May 1915, the German totals might have risen from 127,000 tons in May to 250,000 tons in August (183K actual). At this point the number of U-boats stayed the same until 1916, so we can keep it a a quarter million tons/month for the rest of 1915. Obviously, Britain wouldn't be able to stand up to this ruthless destruction.