OP was accurate, but no longer applies... sort of. Well, if you do this, you have to get the supra tool in order to do 4*. Whereas, you can "skip" the supra tool (cost is about 3.5M on my server for the materia) by having the artisan MH/OH/legs/feet. You'll be 10 craft short. Pop Chilled Popoto Soup for craft/CP. The extra craft bonus will allow you to save one progress step too.
You are correct, except you don't need Artisan Legs and Feet.