Hybrid-role classes always end up getting screwed over in trinity MMOs. Hybrids are all about generalization; the trinity is all about specialization. The worst thing about the early MMOs, in my opinion, was the hybrid tax: even if your role was as a DPS/healer/tank, because you had some cross-role functionality you were automatically relegated to inferior effectiveness at your actual role. The hybrid tax was an early justification for poor balance, which is why you'll almost never find an MMO nowadays that still believes in the hybrid tax: all DPS is equal, even if some of that DPS happens to have a baseline heal (which pretty much always ends up being completely and utterly worthless thanks to not having the gear, traits, or talents when you're DPSing to be anything beyond a token ability).
The JoAT aspect of Red Mage has to come across in the theme, the mechanics have to bring together melee with casting, and the role has to remain specialized.
I could easily see it as a class that bounces between MP and TP consuming abilities much like THM/BLM bounces between chewing through MP and regaining it super fast: you alternate between using TP abilities and MP abilities with relevant "combos" for each. I would expect it to be a DoW class (mainly because it uses leather/chain rather than cloth so it would be using DoW gear along with BRD and MNK) and probably be combo based.
Another way to accomplish the hybrid design would be by having combos utilizing both MP and TP abilities, much like the suggested Cure combo for PLD, wherein you start off with a baseline attack, move into a more advanced melee, and then end it with an actual spell (or attack/spell/attack, but I don't think that sounds as likely). You could even manage to bring in some WHM functionality by allowing the combos to branch out into either a damage spell or a healing spell (so you're either doing full DPS with the casting or trading off your big hit to provide a middling heal; I would probably expect it to be something like an AoE/self heal or AoE/self absorb shield rather than one you have to explicitly target). This construct could use spells that you have to actually hardcast, but I think that would feel more than a bit clunky. I would think that all of the "spells" would be instant casts, at least instant when you're using them as part of the combos.
Going with stances or en-element spells as the core "hybridization" aspect of the class just seems like a cheap cop out as does having spells that are effectively worthless outside of short periods where specific CDs are active. It shouldn't be that hard to have a class that uses the two seamlessly, since it's not like there's a massive difference between a spell and a melee attack on the back end. It would also be a lot more interesting to play a hybrid melee/caster that actually interweaves the two capabilities rather than segregating them.