Setup
Warrior MT, Paladin OT(also assisting healing on eagle) 2 healers (paladin, priest) 1 enhance shaman, 1 elemental shaman, 1 shadow priest, 1 hunter, 1 mage, 1 rogue.

As most people know, the fastest rotation is starting from eagle, to bear, to dragonhawk, to lynx. Having a paladin tank makes the gauntlet event, and various other multi-mob pulls significantly easier, and essentially turns the dragonhawk hatchlings into a laughable portion of the fight. Every boss must die in under 3.5 minutes, and with this set-up, you generally need your melle and ranged to be doing 1000+dps.
With skilled healers most CC is unescessary, save the flame-casters after bear boss and on through lynx.

Now obviously, some of the classes in this set up are replaceable, with a mage being the only
nescesity for spamable CC, but 2 heroisms, 2 paladin buffs, AOE aggro, and the all around buffs that can be added to the raid's DPS, this is one of the best set-ups in my personal opinion, but going in there with a consistent group and knowing every single pull and what everyone will do will be the single biggest time saving factor.
The total time it should take to be efficient on the gauntlet event as well as eagle boss should be around 7-8 minutes, which upon killing him will leave you with 22-23 minutes to get back to bear boss and down him.
Again, with a paladin tank you can basically just have both your healers standing right on top of the paladin tank without worries of pulling heal aggro.
Now again, you could probably replace the holy priest with a resto druid or a resto shaman (one that knows how to use more than chain heal), but being that no one should die, you can just as easily have a friendly druid buff the raid before entering. One shortcut, although minor, is having your raid jump the wall directly below the eagle platform heading back towards bear, and initiating pulling the pat right away. The pulls to bear are fairly basic, but regardless, for any group without full t6, this will realy test your abilities as a healer. You will proabably find that even with a shadow priest, you will use more mana pots on trash than on bosses, and i personally suggest using them as often as available to save any amount of time that would be spent on drinking.
Essentially, you again, should only have spent about 7-8 minutes max doing the trash and downing the bear boss, which will leave you with about 24-26 minutes to complete the timed event. The trash to dragonhawk is where your dps and anything with a stun/slow ability really need to be on point. With the seemingly random and frequent spawning of scouts, most pulls should be done as far away from the huts as possible, obviously without wasting time positioning to much.
Once you have gotten past the first few pulls its very helpful to have a hunter behind the raid with a camera on any path/hut behind them, and a rogue up front watching any path/hut in front of the raid. The best tip i can give to speed up these pulls is that when you are activley dpsing either the trainers/flame casters, your rogue and any other class with a stun ability should do everything to keep these targets incapacitated, the flame casters buff obviously should be removed by the mage, and their aoe fireball spell does some pretty nasty damage, and the trainers are going to cut down the efficiency of your healing/dps if the Mind Control is not quickly dispelled.

Once through the first 2 huts and the trainers, you have an option of going left or straight, with left being easily the fastest way with only 3 absolutely unavoidable pulls, as opposed to about 5 or more going straight. There is a pat going up to the dragonhawk platform that can be avoided altogether, and basically all you need to do to make that work is pull the final group before dragonhawk up the stairs. With a paladin tank, this boss can easily be done in about 2 and a half minutes, basically keeping your rogue and enhance shaman on the boss the whole time. With one healer on the paladin tank, you can release one full side at a time, but you need to make sure you have 1 or 2 peopel quickly kill the other hatcher, and also kill the other one after you release one side of eggs, as he will then move to the other side to continue releasing eggs.
For an obvious reason why having a paladin tank makes this so easy is the aoe aggro, but the time saving ability that really makes this whole strategy is Divine Shield. The hatchlings give a stacking debuff on their target that increases fire damage done on that target, once all the hatchlings on one side have been dealt with, the paladin can divine shield and remove all 40 or so stacks, making it easy to quickly move to the opposite side and deal with the other hatchlings.
NOTE: at 35% dragonhawk will release ALL unhatched eggs, and with a solid group of DPS, you can actually achieve that shortly after the first group of hatchlings is dead(we learned this the hard way by not watching his health) and also at 35% he will hit a bit harder, but its a laughable "enrage".

Now before i mention probably the biggest time saving thing that i know of in the instance, i have to mention something fairly obvious. Don't release any of the prisoners, unlike the loot on the bosses, they will not dissappear, this will save you some time as well. Again, this whole process should only take about 7-8 minutes, so depending on how quickly you were able to accomplish all of this up to that point, you should have somewhere between 16-18 minutes to complete the final timed event.

Right off the platform will be a few pulls, and here is the absolute biggest time saver of skipping trash in the whole instance. Once you disperse the few pats and lynx pulls right outside of Hex-lord's chamber, you will see a hut ahead of you. There is a pat of 2 trolls and 2 lynx, you can skip them but its not really needed. Once they are dead or out of the way, your raid can jump through the window of the hut, walk through, and jump through the other window, mount up, and ride along the wall/halazi's building down to the water where you will start the final pulls to halazi's chamber. This will easily save your 2-3 minutes, which depending on your DPS could make or break whether or not one of you rides away with a sexy bear.
Same thing applies with keeping the trainers stunned here/flame casters sheeped. It is possible to do these series of pulls and the boss within about 14 minutes.
The general order of doing all of the trash in the instance will depend greatly on your healers ability to be mana efficient, and every player using everything in thier arsenal to "haste"ily down all of the mobs.
The best way to do the marking/splitting of the trash pulls with the pally/warrior tank set up is to have the paladin pick up everything, and where AoE is not the best route, have your warrior tank pick up one target, mark it, and dps it down.
All dps should hold off until the aggro is on the tank (obviously) and be prepared for any totems that may arise. One thing to note is the final pull on the bear boss platform can be done with NO CC with 2 axe throwers, basically being done where one axe thrower is Misdirected to the warrior after the paladin uses his snazzy captain america shield throw, and the warrior grabs aggro on one of the bear riders.
This is VERY healing intensive due to the bear rider's debuff, but for any guild thats into t6 content, none of this should be a problem, and with a consistent, competent group, you should see some of your raiders riding bear mounts in no time!