Here's the rule of thumb for Sha P2 -
Never leave more DPS'ers on the adds than is neccessary to kill them before next wave.
Think about that for a second - up till 3 adds, you only have multidotters keep stuff up on them and focus the boss.
When one more add is added to the mix, you add FIVE fulltime DPS'ers to make sure ONE add more dies. That's without concidering passive cleave like diseases, tank cleaves, you get the idea.
Basicly, you're ramping up WAY too fast. You don't need to "assign" people to get on the adds. If they die quick enough, then good. If they don't, then ask people to switch ~5 seconds before sha submerges, and ask another person to help on next wave.
Also - Melee are fine for this fight. I don't know why you would want to avoid having them in. You gain nothing from being ranged on this fight (apart from a slightly higher uptime when he re-emerges far away). Spouts can't go on melee, meaning it's even beneficial to have alot of them (as long as there's +8 ranged targets, if the mechanic is the same as in the "old" days still).
Along with that, melee provides raid CD's most ranged do not - rallying, devotion aura (hand of purity, too), AMZ, Ancestral guidance (when aoeing +5 mobs that thing just heals the entire raid without an issue).
But back on topic of your raid - they're not really underperforming, as such - matching
(your 17:22 attempt, started when lust was popped, ended when people started dying after wave number 12)
(Our kill from yesterday, started/stopped at same points)
You can see that our far superior geared raid (had everything on farm for 6-7 weeks) is only pulling 170K dps more than you.
So essentially, it has to be a performance issue. Someone panics, dies to a huddle. Tank doesn't taunt in time, get gibbed, game over (we use 4 because of this, just to be on the safe side. Have the DPS to make up for it, can't be bothered doing a +15 min pull just to see a tank miss a taunt at 15%).
How do you deal with spouts, Tank debuffs, and Huddle?