Finally hit 20 Exalted Reputations with my latest farm done with the Consortium!
How did I grind this one?
First of all I'd recommend running Mana Tombs until 5999/6000 Honored.
After this complete quests in Nagrand and Netherstorm. You should hopefully hit Revered at this stage or close to it.
Once you have done quests, start to dual farm Mag'har reputation and use the Obsidian Beads for Consortium. It's likely you will hit Exalted with Mag'har first so after this complete the repeatable quest "Another Heap of Ethereals" in Netherstorm. You can usually farm 30-40 badges every 15 minutes, so very efficient as 10 give 250 reputation per turn in!