If the math is right, which I doubt, in 10 hours you can earn 74ish Emblem of Triumph with the random dungeon feature. This is not including the three new ICC dungeons and no raids. Does this seem right to anyone else? Is anyone willing to see if this works in actually instead of just on paper?
Id imagine if you can get the heroics done quickly enough and just keep doing randoms, you can gain a ton of badges sure. Your limitation would be the time it takes to finish each instance, the time you plan to play, and your level of patience on PUGs before you want to /wrists.
If you have a good group who knows the instance and is really feeling saucy, you can keep doing random ones, figure a 30 minute clear for each, 2 triumphs from the random, 3 from the dungeons (the minimum), can get 10 an hour.
Good luck with that. You'll get Pugs that stand in the beam and can't keep brann alive in HoS like me. Took over an hour to finish.
The trick is, to get 4 guildies in a group. Healer, Tank and 2 dps. Pug the last spot, as a dps will be easy to find. You still get the rewards for doing random that way (I think).
You can get a ton of badges, especially if you can pull like a madman. Getting a tank to join queue makes it near-instant groupings, and most dungeons you can just destroy with decently geared people.