Ill write what works for us, might be useable for you too.
Mogu room opens boss>4 small,6medium>boss
Mantid room opens 2medium>small until 22 energy>2bosses
That way we are not overrun by sparks in neither rooms.
On mogu we find it easier to deal with lesser amount of small ones and all the medium ones. On boss remember to kill statues asap. The priority for us is sparks>statue>boss.
On mantid we find it easier to just open two medium and rest smalls. They die to tank/healer buff very fast, plus people help abit by aoeing. The priority is kunchong, but at that point its tank responsibility to get group out of puddles. I usually try to have 4 small ones up at a time.
Oh and last thing, you are saying about standing in shit. Its not your responsibility, its theirs. They need to not stand in bad shit and its their responsobiity to notice things that might hurt, kill them.
On top of that, on your longest try your top dps seems in the same range as ours, your lowest thou. Your hunter really needs to step up abit, unless hes new/undergeared. Shaman/s seems lowish aswell. Frost dk too. The only real thing I see is that you seem to be aoeing a lot more then us. We do have very similar comp and our shamans, paladins and dks aoes are almost last column on world of logs. Maybe you should try more single target approach, with aoe being provided from healers/tanks buff.
But in all seriousness, I kinda would like a more direct questions, like what is actually killing your people and the raid as a whole.
In response to the DPS issue, our Hunter (Me) Frost DK and Shaman happen to be at the other side of the room where there seems to be issues picking up our DPS. Al three of us seem to be able to hit 290k+ and our Frost DK is normally at around 325k so DPS on my side isn't that much of an issue