Just a few thoughts. Some general, some specific
1. Agree wholeheartedly with the parser. Some people (I don't think you're one of them) think parsers are evil and that once everyone's DPS is known and public, the person on the bottom is going to be shamed out of the group. It's only like that if you want it to be. Ask your group to download a parser and get into it so that you know where the "problem" could be. Grob'thok can be killed with 3 DPS and not enrage, so the fact that you have the full complement and hit enrage ~15% without any prolonged pipe smash phases (i.e. the tank positioning was more than sufficient) means it's a DPS problem. And as a good DPS you have to know when it's your fault. If you know who your lowest DPS is, when necessary, you can assign them tasks that allow your higher DPS characters more up-time on bosses. Parsers help you determine who is good at what. And that information is priceless.
2. If you're leading, you need to be mindful of the little nuances of specs. I'm not saying you should know how to play each roll of each member in your group (because that's impossible) but I find it very beneficial to be able to speak with other raid members and ask them what their rotation is. Maybe they are going X-X-Y, when it's way better to go X-Y-X and by having an open conversation about it you'll get some more DPS out of people.
3. Open gear discussion. You're clearing some HM content, so clearly you must be somewhat geared. Make sure the group is aware of which augments are "best", and are trying their best to avoid high endurance mods/enhancements
4. Re: Grob'thok specifically. You spend entirely too much time on the adds. The Jugg co-tank should be able to kill them on his own, with maybe a little AoE help from the Merc, or one Sorc.
Around the 3:00 mark I notice the Sniper using Shatter Shot, but you already have Tracer Missile and an off-tank Jugg, who also appears to occasionally put his debuff on Grob'thok (rotationally) after he leaps back. It's a super small thing, but it's a couple of GCDs wasted, and kind of speaks to general "raid awareness". Armor debuffs don't stack. The merc/jugg will put their debuff on rotationally, there's no need for the Sniper to do so as well.
And see, that's my point. For the Grob Thok fight, we specifically had our DPS turn to AOEing the adds to help our off tank, as the whole raid consensus was that the adds were not dying fast enough in the lava trails and he needed DPS help. This was a Jug tank, if that narrows anything down at all.
So the problem there would not exactly be lack of DPS, it would be the offtank's inability to kill the adds. Which, in pretty much every situation, I find myself attempting to call the problem on something such as "lack of DPS" and discover the problem is caused by something else entirely outside of their control "offtank can't kill adds on his own".
And here we go, I have some logs for my personal numbers to see if this helps. Here are some numbers that we are hitting currently on Corrupter Zero HM, as we have been stuck on him for over 2 months now and just recently got him into the burn phase:
Corrupter Zero HM One of Seven Wipes Raid Numbers (Some players refused to get in, although thankfully, both healers were in the Parsec)
Corrupter Zero HM Personal Tank Mitigation Numbers
One of many of the pulls, as most of them were barely above a minute and not worth reporting.
However, we did manage to get to the final burn phase, where we died from people getting owned by the laser phase:
Corrupter Zero HM Progressive Pull Raid Numbers
Corrupter Zero HM Personal Damage Mitigation Numbers
I am Zuhara, a sin tank, running around with full 78s except for the 72 hilt and have the 2 piece set bonus. Am I taking too much damage in these pulls based off the mitigation stats? The last boss fight is a little high, as I was actually tanking the melee mob with the boss at one point, where I literally only survived thanks to Deflection hahaha