I agree with you that Howe made mistakes & might have stopped Washington cold in this battle.
There were actually 2 Howes. They were brothers. One was a general, the other an admiral. Both were there during the New York battles. I incorrectly stated earlier that it was Admiral Howe who was supposed to have met up with Johnny Burgoyne. It was General Howe.
Check out the PBS series I linked to. It was a terrific one. They only seem to have the first 3 episodes, but they were great.