Why order new? You have the parts you need in the old engine!!!! Getting them out would be good tear-down practice, too, before tearing down the engine you're actually going to use. The parts you need have NOTHING (zero, nada, zilch) to do with the shifting issues you've had, and will not damage the AE engine when they go in.
The shift drum (what the parts fiche calls shift cam) from the old motor will drop into the new motor and POOF!!!!! You have the correct part for an 'A' engine. That whole shift shaft assembly from the old motor will go into the new motor, and POOF!!! You have the correct 'A' parts in place.
When the engine's all buttoned up and back in the frame, you assemble ALL of the external stuff from the original engine onto the side of the new engine. That bracket that mounted all the actuator stuff has to come off first, because it's in the way. The neutral switch (actually the gear position switch,) the shift pedal, the link, and the arm on the end of the shift shaft. The slave cylinder with the hydraulic cable from the clutch lever goes on, and again.... POOF!!!! You have an 'A' engine in your bike. Finish the wiring and plumbing and go riding!
The only reason NOT to take parts from the old engine would be because you have some hope of selling the old engine.