The invasions of KY and PA were done to show the European journalists that followed along with the CSA during those campaigns that the South was serious about the war and to cause a shift of the front to the north which would allow the border states political room to move into the southern camp. The South wanted British help to break the blockade and there is no question about that. The whole Southern strategy was to make the North want to sue for peace becasue the cost was to high to keep the South in the Union. There is nothing to dispute here about that, it is well documented that the South had no designs on conquering the North.
If you really think Lee and Jefferson sat around contemplating how to conquer the North then you are really mis informed about history. Go back to square one.