You know who else took a detour through Gettysburg?
Johnston Pettigrew, leader of Confederate forces that encountered Buford's cavalry on day 1 of Gettysburg.
Admit it, someone thought I was about to Godwin the thread and say Hitler...
From a 1936 start?
Germany, by herself, cannot achieve such a defeat in time for a 1940 Sea Lion even with a massive naval investment in 1936. Sure, the Luftwaffe can bomb the RN all it wants, and Germany can build a real set of transports rather than river barges if she starts early enough, and maybe the BEF can be wiped out so thoroughly that the Royal Army is in terrible shape. But there is no real way for the Royal Navy to be damaged enough to render an invasion possible with just Germany doing it.
Sea Lion can only work if the RN faces a significant defeat at sea. To get that defeat, the Germans have to work with the Italians and Japanese. That means Japan has to be attacking Britain when the war starts in 1939. It also means that the Italians need to secure Malta in 1939 and force the Royal Navy into multiple battles.
I hate to sound like Mahan, but Italy, Japan, and Germany need to force the RN into one or more significant sea battles that result in defeats for the RN. One victory won't cut it. You need multiple defeats like the loss of Prince of Wales. Wiping out the entire RN is not feasible, but with substantial losses, the Admiralty is faced with ugly choices. Either the British spread the RN out in an attempt to continue contesting the Med and Pacific, or they capitulate and let Japan attack Australia, New Zealand, and India with impunity while the Italians hold the Med.
Losing either the Med or Pacific might be okay, but I am not sure if it is politically acceptable to leave both the Med and the Pacific unprotected by capital ships (what would Canada and South Africa think if the RN let the Aussies and Kiwis fend for themselves? What would happen politically in India if India was left bereft of naval protection? What would happen in domestic politics if both the Suez and Singapore fell?). With the RN spread thin, a concerted attempt to attack Britain at home might be feasible if Germany has real transports, the Luftwaffe gets good at bombing ships, Japan and Italy manage to get their navies in place in the Atlantic (similar to Overlord), and the German army is ready to go by sometime in the middle of 1940, before the Brits can replace army losses. In such a situation, there is a real chance of Sea Lion being a threat. (A chance, not a certainty.)
Now, I know Director and few others are about to say, "But Secret Master, the RN will never leave Britain unprotected at home, colonies and Commonwealth be damned!" But that's the trick, isn't it? The goal is to win the war, not to specifically invade southern England. If the RN retreats to Scapa Flow to lick its wounds and the rest of the British Empire and Dominions are given a thrashing by the Axis powers, then I suppose Sea Lion doesn't work.
But now the empire itself is falling apart. You'd have to ask yourself whether Hitler's overtures of peace, including offers to let the British Empire remain relatively intact in exchange for hegemony on the continent, are more appealing as the overseas possessions start to fall like dominoes.
The hypothesis I want to put forward is this: a credible threat posted by Sea Lion (real transports and all the other things I list), coupled with the erosion or end of British naval hegemony due to multiple naval defeats, is more or less checkmate for Britain. If Britain has to choose to either protect her overseas possessions or the Home Islands, its over and they should seek terms.
But it only works if both concepts are in play. If Germany does not have a credible Sea Lion in place, then Britain can weather the defeats overseas. If the combined navies of Germany, Italy, and Japan cannot defeat the RN enough to erode her hegemony of the seas, then a credible Sea Lion is a complete waste.
In short, my strategy for Sea Lion assumes political, diplomatic, and military coordination and insane good luck on the part of the Axis powers that is as much of a fantasy as the fan-boy wank fest you proposed on the first page.