Hey Buddy!
Deaggro skills always depend on two things - how much DPS threat you are doing and how much threat your tanks are producing. So really, it's a two-way street.
From your WWS I can see that your druid starts the tanking rotation - this is very good for threat since the warrior can safely apply all the debuffs before having to worry about threat.
It's true that your tanks can't afford to wear threat gear, that's why you put them in a DPS group (which I see from your WWS that you have also done). ANYWAYS it does look like your tanks could pump out a bit more threat but of course you should use your deaggro spell on Brutallus. It's actually a very fine art.
As a mage you have to consider several things:
a) When to use invisibility. If you use it too early you dump too little threat and it's wasted.
b) Do I let it tick for the entire duration or only 1-2 ticks?
In an "ideal" Brutallus situation you would do so much DPS that you have to use your deaggro spell AND after using it, you'd still be at around 129% threat when the fight ends!
But ok - enough of that.
Having your ranged DPS standing at melee range is just stupid. Use healers/low DPS casters in melee range and warlocks/mages etc and any other high DPS people in range. A good tip for mage (and paladin) positioning is to have them stand FURTHEST to the burn spot. That way you have people that can't remove it close to it and this should lessen running time (and lessen or remove burn spreading).
I can also tell you that you won't kill Brutallus with 8 healers. The try you linked took 6 minutes 25 seconds and you still lack almost 2 million damage.. That's a HUGE deficit. :>
Drop 1 priest, get a high DPS class in. Consider dropping another priest for an extra healing shaman for totems in all groups. You seem to lack decent group setups and alot of drums.
Look on the bright side - you managed to survive over 6 minutes! Now just boost your raid DPS by about 7K and you have a kill! GOOD LUCK!