Going back to my original statement, ie, that without Materia being an issue, you could go through this in a week.
That wasn't a boast. You would need about, three Alexandrites a day, if my estimates are correct. You get one from doing an expert duty roulette, which takes maybe a half hour. That leaves two to farm per day via either Fates or a map. I don't know the drop rate yet, but even if they had the same drop rate as Atma's I think I could manage that, if I wasn't doing anything else.
The only question mark is, how long it'd take to unlock higher tier melds. The failure rate wouldn't factor in this because, again, this is assuming no gil or materia limitations.
This statement was meant to demonstrate that the amount of, "work," involved in this, could very easily translate into less work overall than the Animus books. RNG may not have played a role in that, but, there's not exactly a lot you can do to compensate for needing 1500 Myth tomes per book.
With Novus at least, you can buy your way past varying degrees of the work, if you want it enough, and have the resources.