If I were to take a random shot in the dark:

Atma - 3 days
Animus - 18 days (assuming 2 days per book due to FATE camping)
Novus - 7-21 days (Assuming infinite Gil/budget Relic and luck with the FATE farm)
Nexus - 7-10 days (Assuming full time light farm)
Zodiac - 7 days (that RNG)
Zeta - 7 days (according to a live letter, apparently)

49 days (7 weeks) to 66 days (~9.5 weeks)

If you have a Zodiac already, you can light farm while getting KIs for Zodiac, helping reduce that time greatly.