Hmm, while I give you props for trying... I dunno if this really fits the Red Mage motif.

To be honest I think your confusing Red Mage for another completely different class. Mystic Knight if I'm not mistaken. Sounds alot like it anyway. With your magic empowering your attacks n such.

Red Mage is really supposed to be, at it's core, a melee fencer who is able to cast low-mid tier black magic or white magic.

Not sure how they'd go about implementing this properly though. Doublecast has to be there for sure somewhere. Best I can think of is combo's that allow you to insta cast certain spells (fire/cure etc) maybe with a buff to their dmg to keep them competitive... or w/e i dunno. ;P