I take two issues with unprincipled peter's points.
First, there really were not many native born Americans around at that time with military experience. Native born Americans only fought against the Indians, or as sort of auxiliaries to the British as Washington did. Since the POD is Washington being killed on Braddock's expedition, instead of not going in the first place, you can't even replace him with some other Virginia militia officer. This is why the Continental Congress gave jobs to so many foreign adventurers like Lee in the first place. They really had no other alternatives until competent American officers, who generally had no military experience prior to the war, emerged during the war, and there were not that many of these either.
Pretty much Washington, whose Seven Years War experience was not even that impressive, was their only option. The alternative was bringing in a non-American adventurer.
Second, and this is not as germane to the discussion, but Washington really wanted to wage a more aggressive campaign after 1778 and in particular he wanted to attack New York. Keep in mind that in 1778, the British withdrew a good part of their forces from North American and evacuated every place they held except for New York, Canada, and Florida (there were some attempts to get another invasion of Canada underway that Washington was in no position to help that fell through for one reason or another). But he needed the French navy. For sound strategic reasons, the French Navy focused on the West Indies and in supporting the Spanish in Gibraltar/ the Western Mediterranean.
After 1778, the war became a global war between the British on the one hand, and the French and Spanish (and Dutch and Mysore) on the other and North America was one of the more secondary of the secondary theaters. The only thing Washington could have improved on his OTL performance was to trust Arnold less and to get Congress to give back pay to the army, in other words, not much. Before 1777, a more competent commander might have improved the army's supply situation from what it was not not gotten knocked around as much in the 1776-7 battles, particularly around New York, but I don't see where the Continental Congress could have found that person. It certainly wasn't Charles Lee.