I think the REAL Longstreet is hidden from us by a curtain of time and "interpretations" but if you can penetrate the screen you'll find a man who was not very likable and not even very intelligent.
You could start with this video and it will drop other names of sources you can pursue.
Even though KILLER ANGELS portrayed him as a likeable, wise, solid figure, totally un-appreciated by Lee, the reality is that Longstreet was often argumentative, often criticized and often disagreed with Lee. Gettysburg was not the first nor would it be the last time his personality got in the way of loyalty.
As far as whether he was "right" there is really no sense in asking that question since Longstreet had nothing more than a very hazy concept about "sliding to the right." Missing was his concept of reconnaissance ahead of this move . . . or even whether the exhausted cavalry was able to penetrate through Yankee lines and operate in open ground, screening a Confederate move towards Washington.
Also missing was his concept of how the Confederate Army was to be supplied in such a move. What would be the Line Of Communications? What roads would the Trains use? How would the Army defend its Trains from a Union envelopment?
The wagon train of just one Confederate corps occupied 12-15 miles of road. As one study I saw described it, had the trains all been on the same road heading north, they would have occupied one-third of the distance between Staunton, VA and Gettysburg. During the concentration at Gettysburg, the three Corps Trains and the Army's Reserve Train (itself 15-20 miles long) crowded into the Chambersburg-Gettysburg Pike interfering with troop movement.
At the end of the first day, the Trains grew even larger as casualties poured in.
So any movement south towards Washington had to resolve the issue of how to deploy and protect the Trains and how to keep the roads back to Virginia open.
Personally . . . I think it would have been impossible for the Confederates to move towards Washington after July 1st.
Amateurs think Tactics, professionals think Logistics. Lee was a professional. In many ways . . . Longstreet was an amateur.