More than likely you will upgrade your Relic into Zodiac in stages.

The first being maybe 900 Myth Tomes, +item drops from Ex Leviathan, and Ex Thornmarch


Q11: Will we be able to upgrade our relic weapons to accommodate the increase of the maximum item level?

A11: You will be able to upgrade your relic through the “Saga of the Zodiac Weapons.” While the whole process will be very long, the appearance of your weapon will change if you upgrade your relic weapons up to a certain point.

^^Answering your "In Stages" like being able to upgrade all your Relics into Zodiac Stage one, if you will <-- My Thoughts.

Q19: With item level 90 equipment, just how far can you go from a content perspective?

A19: I believe you’ll be able to clear Leviathan extreme and Good King Moggle Mog extreme with all item level 90 equipment. You’ll want to get the equipment that drops from these battles for...well, I shouldn’t say any more right now!

^^ and with this leads me to believe you will need your Wpn from both Leviathan and the Good King to complete the Zodiac Wpn Quest.