The only way I see Red Mage working while staying true to it's roots is:
- DPS, melee/caster hybrid.
- Uses both TP and MP, alternating between melee and magic while the other recharges.
- En-spells are stances; one buffs melee damage and regens MP, the other buffs magic and regens TP (and swaps STR with INT and skillspeed with spellspeed).
- Has one or two Clemency-like heals, not anything that can replace a real healer but useful utility.
- Has Refresh. Because.
As for Blue Mage... there is a precedent of them needing to be hit with attacks to learn them, so one could see a tank that builds up stacks upon taking (or blocking/parrying) hits that can then be spent on Blue Magic skills.