Some very intersting and inciteful comments. Id say the turning point came about 1938 or so. Germany's decision to focus on tactical support made the LW unsuited to sustained air operations, in which direct support of the armies was not the focus. The things the LW did well were related to support of the army, whether that be CAS, air superiority over the battlefield or tacair ops just behind the front. Later in the war they were able to adaprt enough to make a decent showing of air defence issues, but on the offensive, they were simply out of their depth as far as taking and holding air superiority over a wide and deep area like SE England.
This can't be a turning point in the BoB because at this period (largely before 1938 ) the Germans were developing an air force to carry out precisely the things which you correctly say it did well. In the numerous surviving specifications and other 'doctrinal' documents this intention is made clear. There was never any plan to take on Britain. When such a need arose the German planning isn't just inept, it is sometimes laughable.
The Wermacht as a whole seems to have viewed crossing the English Channel as it would a rather wide river which the Channel certainly is not. The Duke of Medina Sidonia found this out in 1588 as he and his ships were swept past the Isle of Wight and the entry to the Solent!
Cheers
Steve