There's very few things that can go wrong in P3. Sadly, it's not easy for us to tell from logs which one it is. Worst to least:
1: Are your demolition craters being soaked?
I see some deaths due to erupting slag craters; This can both be because you are too slow at moving (you need the raid to be positioned BEFORE blackhand activates the craters, or people are gonna take atleast half their health in damage standing in it, which kills), and because you fail at getting the demo's soaked. If soaking is not an issue, a quick and dirty fix to up your survivability is to mark someone reliable in P3, and have him move the raid around, making sure to keep distance to craters.
2: Are your Impales/Slag bombs fucking up?
If they overlap on people, that's usually an instant oneshot. Can't happen. Get the addon Blackhandassist (plugin for bigwigs -
http://www.curse.com/addons/wow/bigwigs_blackhandassist ). Make sure everyone in the raid has it. It'll make bombs yell "Middle" and "back"; This assumes the tank will always be at the front with his bomb, and tells the 2 random targets where to go. If we're strapped for space, our "back" bombs literally goes out BEHIND the raid instead of trying to line it up (you might be standing right on the tangent of a crater, so no space for 2x bombs without either being inside crater or overlapping).
Marks will yell "left", "middle", "right". Assuming you go around the room clockwise, have left be your decision maker. He positions himself outside of the raid as close as he thinks possible, and middle/right lines up after him. No shuffling around.
3: You have too many people taking massive shattering smash. On all the +7 min tries I check, you have 6 people inside the smash; Your two DKS, two rogues, and two tanks. That should be 4 people.
Why are both tanks taking it? One of you will inevitably always have the slagged debuff, which means you're gonna be taking some spike damage there. How the flow of the fight should be for tanks/melee is:
Tank1 has boss faced out towards the edge of platform.
Boss throws bombs.
Tank2 taunts boss to turn him around to face the middle. Bombs go out to the left.
Boss throws out marks to the right.
Boss, still facing middle, does smash on Tank2+3x melee dps (2x rogue/1x DK ideally in your case). While boss is doing the throw of impales/smash, Tank1 should be moving a long the rim of the platform to next position. When Tank2 goes flying, Tank1 lets boss run as far as he can after Tank2, then taunts the boss. This ensures ~10 seconds of zero melee hits because the boss is pingponging, giving the healers more of a breathing room. Repeat untill boss is dead.
If a smash-soaker has debuff and can't cloak/AMS, call a backup warrior/DK in; A debuffed target should never soak smash.
Essentially, if you and your warrior are BOTH taking the smash, your positioning must be absolutely CHAOTIC to say the least in that phase. This way, the boss will move in the same pattern all the time as illustrated on this map:
http://imgur.com/igwOFJV (and yes, I am completly incapable of supplying good visuals. Bad = Craters, blue lines = tanks flying and taunting around (so the bomb-tank would be moving between the different points of the blue line on the outer edge), and green is the small area where ranged essentially never has to move from the entire encounter.
And that's really about it; the fight can easily last ~8 minutes for first kills, so I wouldn't say speed is your issue. Just need to get everything down smoothly. If what I believe is true (that your tanks are both flying and then has to drag the boss to the edge while trying to tackle bombs), just doing what I explained will already help ALOT by making it less chaotic.
A few pointers on Debri waves -
If you imagine the platform is a clock, with 12 at the top (the sharp point), any debri that falls anywhere between 2 and 11 has to be properly soaked on the first go. 11, 12 and 1 are less important, because they'll basicly overlap with your first smash before any craters are active, anyway.
Likewise, on debri #2 and #3, if any debri falls near the melee, ignore it. DO NOT have them go soak it. It's a waste of a cooldown; you'll be placing a crater right on top of there in a few seconds with a shattering smash anyway, so the space saved is minimal.