This is possibly the best idea I've heard yet.
Loot Specialization:
"Vanity", "Cosmetic", or "Old Stuff" - would drop difficult-to-obtain items specific to your character (warrior has a chance to get Naxx warrior tier, very low chance of glaives etc).
"Consumables" - drops flasks, feasts etc
"Crafting Mats" - drops hides, trillium, golden lotus
"Mounts" - self-explanatory
"Pets" - ditto
"Gold" - a substantial amount, not piddly 30g
"Reputation" - rep (maybe a BoA use item) with any faction you don't have at exalted
Edit: Making this a loot spec option rather than buffing the role-specific bags would attract good DPS as well as tanks/heals, but it doesn't really solve the problem of AFKers. Maybe tie the chance of getting a drop to how well you performed? Though that does open up abuse possibilities.
Edit2: The bonus valor idea might work, but I don't think granting valor above the 1K cap is a good idea because then normal raiders are forced to use it to upgrade their gear.