You need to adjust the position of the ignition switch, the possitioning and likage to the key cylinder mechanism is real touchy! Ignition switch has slots in the mounting bolt area that allow it to move up and down the steering column. It has about 1/4 or 1/6 inch of play in it. It's enough to cause and fix your problem.
Also, there is some linkage between the key cylinder and the NSS switch that can get out of kilter, but for the starter to ingage it has to be the ignition switch bolted down in the wrong spot to cause that.