Nobody has ever proven that there was ever any communications between Booth and the Confederate Government. Even in this letter as you stated Booth was awaiting "word from the Richmond". That is only a one sided statement from Booth and could have been left by Booth as part of the conspiracy plan. The fact that Booth acted did not mean that his actions were the wish of the Confederate Government, which at the time of Lincoln's assination was on the run and in hiding trying to make their excape. In fact April 1865 was the last chance to assinate Lincoln and blame it on the war and the South. Lincoln had served his purpose and had outlived his usefullness as far as the abolishionist and Radical Republicans were concerned.
So was the assination of Lincoln a Southern Plot? We don't even know if the man killed in the barn was even Booth. Yet in the comic books of history taught in our public education system, judgement is made and the South get blamed for what could not be proven in a court of law.