So, there's a few things that you can do in T11 to boost your DPS.

The first one is the most costly, but is also the biggest increase you can get in ALL of FCoB and that is investing in HQ Ruby/Topaz accessories melded with (at the very least) VIT/STR. This gives you the best of both worlds, enough VIT to comfortably survive off tanking all of FCoB and a large amount of STR that the VIT accessories don't have attached to it. This is the best possible way to boost your DPS and I would recommend any WAR progressing in FCoB to invest in them. Ruby accessories come preloaded with +16 SS per piece, allowing you to achieve the 9 hit Berserk combo with only a few pieces, so (to a point) those are the better option. Obviously if you don't need all the VIT they provide, you can swap some pieces out for pure STR accessories.

The second is that the cleave Kaliya does that needs to be split between the tanks is on a set rotation. It comes at very specific parts, and is the only time (in the first/second phase at least) that the OT needs to be in front of Kaliya. So if you do get down the timing for when they come, you can drop Defiance and stand to the side. Obviously you'll want to be in Defiance for Secondary Head swaps and have an IB ready, but aside from those two mechanics you don't actually need to be in Defiance in front of the boss. This changes in the last phase because of the tethers, but your DPS will increase substantially if you stance dance during the first/second phase.

The final one is knowing when you can and when you can't use BB. There are times (many of them really) in T11 where Path is completely unnecessary, so dropping Path for a rotation and using BB when it's safe will give you a bit more DPS.

All that said, your DPS on T11 shouldn't come at the cost of consistency. If your group is clearing the fight then I'd recommend against doing the second suggestion as it can go horribly wrong if you happen to mess it up. Ruby accessories help loads so I'd say those are great to invest in regardless, but don't go crazy and spend all your gil if they're unnecessary for your group. Always remember, you're a tank first and a DPS second, if you need to go 30 VIT, full VIT accessories, the whole 9 yards to survive the fight then that's what you have to do. This, however, is really only the case for MT of T13 and even then only with lower end gear. So the best advice I can give is invest in Ruby accessories and you'll be happy you did... until 2.5 when they're replaced with i110 crafted accessories!