The 3.1 patch is going live in a few hours so before then I'd like to take a few minutes and explain a few changes which will help accomodate how the FC will handle the new content.
First off is the Diadem exploration missions. There is unlikely to be a need to reserve or schedule the airships. We will have 4 airships available for the exploration missions and each airship is locked out for 20 minutes after a group enters the Diadem. This means we can have ~32 people entering every 20 minutes. At most people will be waiting for around 20 minutes assuming they will be challenging the Hard version of the Diadem.
Keep in mind that the FC airships allow two advantages over the independent airships in Ishgard. The first is the ability to organise a full alliance and the second is the availability of the Hard mode monsters. If you do not need either feature and cannot wait for an airship to come back, consider using the Ishgard airships.