If I remember correctly, Hitler's decision for more fighter/bombers actually helped delay the deployment of the Me-262.
Also, I disagree that the Stuka could fit the bill as a prime tank buster. Even if it's an accurate platform for bombing, the Stuka has a very low probability of being able to reach its target given heavy fighter opposition.
I agree that for the Germans to perform better in defensive air operations, they would have entirely transform the thinking of their fighter pilots. This would be difficult given Goering's historical tendency to insist on having his own way.