Chattanooga sealed it.
Once U.S. Grant took Vicksburg, and then was placed in overall command, the question was only "when" the north won, not "if".
It was U.S. Grant's victories in the western theater that decided the war, the eastern theater simply garners more attention. One was a true "theater" of war, the other was simply a series of indecisive battles taking place over a less than 100 mile stretch of ground.
While I agree with you from a tactical standpoint, I disagree from a strategic and political standpoint. Had Lee won at Gettysburg the political climate would most likely have forced the north to sue for peace on terms recognizing the south as a soverign entity. I don't beieve the morale of the north could have tolerated another major defeat in the eastern theater, especially if Lee had followed up a victory at Gettysburg with a march against Washington. Sometimes political considerations mean more in a war than pure military might. For example, the US never lost a major battle in Vietnam but still lost the war.
I agree with your overall assessment, but a Federal defeat at Gettysburg, with the possibility of a Confederate advance on Baltimore, Philadelphia, and/or Washington DC would have resulted recognition of the Confederate States by Britain and France and, ultimately, I believe, in a Federal surrender and the end of the war before Grant and Sherman could have come East to save it.
The other possible turning point might have been a more successful delay in Sherman's advance against Atlanta by Joe Johnston. It's possible (and the subject of several "what-if" novels) that such a delay of the Fall of Atlanta and the March through Georgia might have resulted in a McClellan administration and a cease-fire that would, in the end, have led to separate countries.