Chemist!
They would be "casters" but rather than casting spells, they use their cast time to mix up Salves/Poisons/Potions/Drinks that allow them to infuse Aether (MP) into items for special effects that are not otherwise available to normal items crafted by Alchemists (this is how they can handwave the similar names). So although they aren't casting actual spells, their casts would still cost MP (to keep things uniform between healers). Weapons would be Maces.
Their gimmick could be "Mix", which would be similar to Mudra/Ninjutsu. Basically you learn 4-5 "Mix Components" (similar Jin, Chi, Ten) and mixing in certain order creates a "Charge" of a specific effect (similar to drawing a card, but not random) that you can use at any time during a fight (rather than Ninjutsu, which needs to be used immediately. So you can mix say 3-2-1 which gives a "charge" of a Megalixir (AoE oGCD heal), then in 15-20 sec or whenever "Mix" comes off CD, you can mix a 1-2-1 and get a charge of "Bacchus Wine" which is single target Damage+10%. Then during the fight when you need these skills, you pop the abilities. Maybe you can store 2 at a time for tactical use.
GCD Spells:
Salve=Basic heal
Hi-Salve=Strong heal
Mega-Salve=Moderate AoE Heal
Poison Fang= DoT
Venom Powder= AoE DoT
Bomb Fragment= Basic damage spell (Ruin)
Phoenix Pinion= (Revive)
Arctic Wind= Basic damage spell (instant cast; Ruin II)
Red Fang= Upgraded damage spell (Broil)
Spider Silk= AoE Bind(Tribind/Tether yo!)
Stardust= AoE 200~ potency diminishing (equivalent of Holy/Gravity)
Mixes (could probably rename these so they sound more sophisticated than their FF5 counterparts)
These are your "mudras"
Power Drink
Speed Drink
Magic Drink
P-S-M= Megalixir (oGCD AoE heal)
M-S-P=Lilith's Kiss (Damage+HP/MP Drain)
P-M-S=Bacchus Wine (single target damage+10%)
S-M-P=Triple Star (Next 3 GCD are instant cast)
S-P-M=Light Curtain(AoE damage-10% bubble)
M-P-S=Lunar Curtain (AoE regen)
oGCD's
Itemagnifier=Boost next Hi-Salve/Mega-Salve potency
Pharmacology= Basically kissatsu for CHM (reset Mix CD)
Chocobo Feather= Haste+5% on target
Hero's Drink= Healer LB3
Obviously it would need to be tuned to be balanced but it would be sort of a blend between NIN's Mudra system and AST card system, while utilizing familiar items from throughout the FF series for a wide range of effects.