One thing to note about your logs overall: once you are going to wipe, whoever is logging for you should use the wipe command in the AMR addon. /amr wipe - that will make your infographics a little more useful for things like DPS, HPS, etc, since it cuts off anything after that which is really "garbage data" since the fight is already messed up.
Looking at your best attempt where you got him to 6% (since that will have the best data for DPS/HPS), your raid is pretty low damage. We were having problems on this fight with healers running out of mana in the last phase and everything going bad. So, we actually changed it up and removed one healer and added a DPS and the fight went way better for us (in particular we added a DPS that could do heavy AoE to the packs). At your current gear level, healers just aren't going to make it much past 10 minutes. Six healers for a 21 person raid seems like overkill as well. I'd try it with 5 healers if I were you, and work with some of your DPS'ers to get their damage up to shorten the fight. You have a few really good players carrying some much weaker players (which is very common). Unfortunately our forthcoming tool that can help individual player performance isn't quite done yet
You'll have to help them the old-fashioned way: have the raid leader yell at them to get better.
You guys aren't really doing that bad on avoidable damage overall. Others have pointed out some of your weaknesses that the infographic helps highlight for you. Shave 30 seconds off your fight and don't get pinned down and you should see a kill relatively soon.