I'll second what was said above - do this fight with 2 healers. The extra DPS shortens the fight, making it much easier to heal. The longer this fight goes, the harder it gets.
Also, do not try to solo-tank it without a mortal strike effect. I did, and it didn't work, even with all our DPS well over 5k. He just heals himself too much.
My guild took this guy down first try with no deaths. We generally have a similar melee-heavy setup as the OP but rolling with one tank and 2 healers made it extremely easy.
Blood DK (Tank)
Fury Warrior (Offspeced tank)
Ret Pally (me)
Blood DK dps
Boomkin (Offspeced healer)
We had the ele shaman drop earthbind totem and ranged kited the adds, had no problem taking them down in time to switch back to dpsing the boss. Tanking the adds instead of kiting them would increase the blood power DS gets drastically. With all the extra dps, we killed DS shortly after the first mark. I'd say go with one tank and have one of your healing priests switch to shadow for the fight and you'll find it's a lot easier.
On Saturday we spent a good chunk of time trying to figure out the best way to kite everything. Between a hunter laying her trap, a boomkin agroing and kocking stuff around and a Warlock laying down (a very effective) shadowfury. after about 2 hours our best attempt was 6%. Very close but the healing just became to much of an issue.
Sunday, we decide to screw it. We tell all the dps that kiting is dumb, everyone stays on the boss, when the adds pop out the warlock hits shadowfury, and all dps goes nuts on AoE. Including tanks who pick them up. The mobs were only getting 2 swings off at the most. Usally none. We only had 1 mark go off which the holy paladin easily took care of.
We 1 shot him with no deaths and get the achivment. It was really easy.
you dont even have to kite the adds in 10man i have done him a few different times because our 10man raids are usally Melee Heavy or just decently filled with enough range and melee... but wen we are melee heavy all we do is have a Ret paly Stun the add on the right all melee BURNS that add since he cant melee anyone bc he is stund he wont add and bloodpower to the boss. Then if we have at least 1 range just have them try and kite that mob long enough for melee to kill first add and then they all go after the one being kited my the range on 10man u dont need to kite soo much as u do on 25man bc its very simple stun and burn.....
Secondly, you can stun the beasts for 9 seconds. (Shockwave+CB). That should be plenty of time to dps them down. Your warrior tanks needs to wake up, and save stuns for adds.
Have melees focus on left add, ranged on right, pally can optionally help out with his stun, but shouldnt be needed. Fury warrior has hamstring, dk has chains of ice.
I have done this multiple times with only 2 ranged people, with no problems.
I am the spearhead. I am relentless. I am the last line of defense. I am a Warrior.
Just wanted to mention:
1. Keep your disc priest - powerful shields can almost trivialize this fight. Damage prevented does not generate BP. Shield people with boiling blood to negate that, shield people who might get hit by adds to negate that. Extra shields can help negate the novas too. With a disc priest and fast tank switches, you can do this fight with zero marks going out.
2. This was mentioned before, but prot warriors can shockwave an add to help out. Even when they are tanking, just pick one side and face a little that way, when the beasts pop up, shockwave them and the dps should have no problems burning them down. When we have 2 prot warriors, we each do one side.
3. Rogues are good on the adds too - just have them tricks to a ranged dps and toss in some stuns.
Since you're raid comp includes running with two Protection warriors, I would recommend the following.
1. Have ranged DPS focus on and kill one of the adds. The elemental shaman should be the one to pull agro and can use Frost Shock and Thunderstorm as needed in order to slow and knockback the one being killed by range.
2. Have your tanking warriors stun the other add with Shockwave. Since you have two warriors, you have two shockwaves, this gives you a full 10 seconds. The melee DPS can burn the target down quickly enough. The tank can accomplish this by turning slightly so they are tanking Saurfang at a slight angle so they are able to stun the add when it spawns. You can tank the boss with your toon at a slight angle so the boss is still in front of you but you are also able to hit the add when it spawns. If your 3 melee DPS all switch to the add they should be able to burn it very quickly.
Don't leave killing the Blood Beasts just to your ranged DPS, have your melee take out one of them as well. That will significantly lighten the load.
Have your shaman use an Earthbind totem in the centre, with the healers at the back. Make sure your tanks/melee dont use AoE abilities when the adds come out. One chain lightning should aggro them. If they manage to get to the heals/ranged, just use a knockback on them. Also, I find it better to 2 heal this fight, especially if you have a disc priest for Boiling Blood.