<snip> I think you're come up with as positive result for the Germans as is likely to happen (I don't actually think the LW could achieve Air superiority even in a small area as they would covering two forces at once here)
Air Supremacy, not just Air Superiority, over the Channel AND over the sea and air landing zones is an absolute requirement for Sea Lion. The Germans literally cannot afford to lose a single ship or barge, right down to the last minesweeper. You need to have unescorted German bombers roaming the British skies at will at least up to that point.
North and west of that, you'll need solid Air Superiority all the way to the Thames River and over Southampton. Air Parity is acceptable for vital missions north of the Thames but ultimately still in German fighter range. Mind, this last point assumes eventually seeing German field airstrips in SE UK.
Air Supremacy, as stated, is your aircraft going where they will unprotected and unmolested. Think the Germans in Barbarossa D+7, Japan over the Hood and Prince of Wales, or the Allies over Normandy on D-Day. An enemy aircraft penetrating an umbrella of Air Supremacy is suicidal, but on rare cases it could be done (the two Luftwaffe Me-109s strafing the D-Day beaches over Gold and Juno, frex). The attack and shooting down of a Japanese Kate bomber by a sole surviving Wildcat fighter during the second invasion of Wake Island is another. (1) Though the American did NOT survive his attack.
1) Karma Alert: The Kate that Marine shot down was the aircraft and crew credited (at the very time of Pearl Harbor) with the destruction of the USS Arizona. Their fellow aircrews took it as supremely ominous. One surviving veteran said: "It was as if the spirits of the Arizona reached up from the sea to pull them down...!"
Air Superiority, OTOH, is being able to effect air missions where you will, but with the need of escorts and an understanding that the difficulty to maintain mission success gets harder the deeper you go into enemy airspace. Think the Battle of Kursk, the Battle of New Guinea, North Africa (in the later stages), Sicily. Burma, depending on the time of the war.
Air Parity means your air force and the enemy's are duking it out right on the front itself. Battle of Britain, advantage of numbers to Germany, home field advantage to Britain.