Mythic weapon quests are beyond ridiculous. Read the alexandrite discussion page on FFXIcyclopedia for a good, cynical laugh.
This weapon takes a minimum of at least a year of nonstop, hardcore, only-mythic-weapon-minded play:
http://wiki.ffxiclopedia.org/wiki/Aymur
This weapon takes a 2~3-hour reive:
http://wiki.ffxiclopedia.org/wiki/Hunahpu
(Note that thanks to the item level, it also levels pets up to stats congruent to level 115)
And other, even better weapons, take a 45-minute Delve.
I know level 99 mythics are going to be powered up, so make the level 100+ versions take a year and make them worth that year.
But the level 75 steaming-piles-of-monkey-**** versions of mythic weapons need to take less time.
It's "Duties, Tasks, and Deeds" that needs adjustment most. No level 75 mythic is worth what they cost. Right now, few of the level 99 versions are.
Part 1: ALEXANDRITE
Alexandrite can go to hell. Why does the EMPRESS of Aht Urhgan have a single mercenary paying out of pocket to satisfy her lust for things that glitter? If I'm the Empress's sugar daddy, she needs to start returning the favor. Empress Nashmeira is the worst gold digger in the history of videogames. I hereby dub her "Goblin Gold Digger."
Even if you consider the current level 99 reward, the alexandrite portion of the quest should be a maximum of 5,000. You could easily get a far superior weapon in a reive anyway. If you want to consider and honor the harrowing legacy of mythics, it still shouldn't be above 20,000. That's more than sadistic enough for anyone's sick pleasure.
Part 2: THERION ICHOR
Cut this down. Major time sink.
Part 3: NYZUL TOKENS
I feel this part is fine, honestly. It's the least painful part.
Part 4: JOURNALS
Let players spend multiple tokens to lowman assault (examples: spend 3 tokens and you can solo one mission, or spend 2 and you can duo a mission). This isn't ridiculous and it would actually SPEED UP 80-90% of assaulters' progress through those missions. Finding 2 other people to assault with for 50 missions (100 missions if you count prereqs) is like posting on the official forum asking for mythic adjustments.
Oh wait....