Thank you!! I've been trying to figure this out all day.

My airship is now rank 7 and I already switched out two components from Prototype II (crafted all but limited at 18/18 component points right now. Rank one is 3 per piece and rank 5 pieces are 6 each)and unlocked Prototype III and couldn't figure out why I couldn't make another airship. Prototype III starts at airship rank 15.

Also something to note, when you add components for the rank 5+ you get back your rank 1 stuff. So you would technically be able to use those bound pieces on another airship.