Two thoughts seem to stand out to me on the "Enhancer" role for Red Mage:
1: Most of Red Mage's enhancing spells are self-target.
2: Red Mages don't need any more cycles.
One possible solution to both:
Job Ability: All for One and One for All (maybe too long of a name...)
As long as the Red Mage is hitting a target with their weapon, they produce an aura that copies all buffs on themselves to other party members around them.
(potential sub-feature... Red Mage may gain the benefit of self-target buffs of other party members, such as when a Monk uses Focus/Dodge, the Red Mage would gain accuracy/evasion too. Berserk when Warriors use berserk, etc ... and when coupled with the Red Mage's buffs copying to the others... anybody's self-buff now becomes a party buff! Demi-gods anyone? Would need to look at all the potential combinations to see the real potential)
Now, all their self-buffs become "AoE", there are no cycles (except Refresh for the mages who aren't in the aura range), and they get to melee monsters as a bonus.
~*~
They could obviously use new enhancing and enfeebling spells, if they're going to live up to the definition provided by SE in that vision, but it's a good start with what they already have. And yes, I tied it in to the Melee side of Red Mage (without breaking with their vision!)

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