You have HoT timers wrong, they start at 0:40 and there's 40s betwen each hit. 7th HoT is on 5:20. Usually we leave our Holy Pallies on that one, so they can keep spamming HR on everyone once they get out Twilight realm. Just bubble the damage - obviously they'll have to skip 5/6 HoT in order to make it.
Aura Mastery doesn't work, damage cannot be resisted. Spend that GCD on another Radiance.
Using DPSers Tranq/Divine Hymn should only be considered as last resort. It will drag out the fight, meaning you might not make the timer, or simply take this overwhelming damage for few more seconds. Feral 4pc is an exception, especially if they get Thrall buff - 40 seconds duration will cover majority of critical damage phase.
GoAK on +healing people is quite good, especially when paired with Wings and maybe Volcanic potion.
Divine Hymn as Disc is fine, especially since you should be using Red buff and Heroism. (and unlike DPS tranq, it offers +healing) Just drop a Barrier and use Hymn, that should cover 1:00-0:50. Along with Heroism and something minor to help out (AMZ/shout), you should last till 0:40 without losing Bronze buff.
Keep in mind that there's few second break after each HoT - I think AOE starts again at 0:33, so don't just use cooldowns on 0:40, it's precious seconds wasted. Prot Pally can cover 0:33-~0:20 and after that... well, you're screwed
SLT isn't all that great here, so you're pretty much counting on DK 4pc and Bronze buff to keep you up until the end.
Get a 5th Healer - preferably another Disc. Pally is kinda meh (meaning, still good but not nearly as godly) without Blue, doesn't offer any cooldowns, Shammy SLT is only 10%. 2nd Barrier would be ideal, but anything might work to help out, even Tranq with Red. If you're worried about Berserk timer - have 2 healers DPS for first 3 minutes. It might not seem like much, but it can be >5mln, which is quite a bit and you don't lose any healing in last minute that way.