Firemages deal 12% more damage versus targets below 35%, Afflocks deal 12% more damage versus targets below 25% - lot's of other classes got similar talents/abilities to deal a large amount of extra damage during the "execution" phase and a bunch benefits from haste. If you got a two minutes cooldown and a three minutes coodown you can blow them at 0/0, 2/3 and 4/- during a six minutes fight or line them up to deal more damage, 0/0, 2/-, 5/5 during lust and your second potion. There's only one thing you can't control: trinket proccs. They'll likely be up at the start of a fight and due to different internal cooldowns and various procc chances and ppm you'll have a hard time having all of them up at the same time later on.
Stating that with ilvl 380 their dps should be doing 30k dps on ultraxion is hard, imho. We killed him in full heroic firelands gear, two caster legendary and some lfr + 397 pieces (avg ilvl ~ 395) from the first id with an average dps of ~33.000 dps on our heroic kill. Yes that value is ~10% above your estimated value but depending on the class and rng (hello fading light) some players/classes will have a very hard time hitting your numbers even on normal mode, "playing perfectly" isn't a good benchmark. You're raiding 10m as well, don't underestimate other influences like raidbuffs. 6% versus 10% spelldamage is a 400 spelldamage difference easily. What happens if you don't have replenishment or some major melee buffs are missing?
Quinafoi gave a good hint, moving to two healers can be very useful. Even if your third healers plays subpar and only adds 15k dps, this decreases the burden on your 5 regular dps by 3k each!
@ your logs:
Sadly your hunter just suck, simply as that. Serpent sting had 50% uptime on most of the longer fights and he must be focus capped all of the time. Tell him to at least hit his chimera shot when it's ready, 5:26 fight length and 14 shots - 6:05 and 12 shots - 5:39 and 7 shots - .. the list goes on. And have him use a pet that brings something benefical to the raid like 4% more physical damage taken.. and playing Marksman without melee haste? If he'd play survival instead all your other melees (feral + fury + rogue + both tanks) should see a HUGE bump in their dps (increased energy regeneration, more autoattacks -> rage, more proccs, more dotticks and so on) and imho it's rather easy to play.