Kinda long but hope it helps
Talent/glyph setup:
Talents:
Soul Leech - Could use Dark Regeneration if your healers struggle at specific points, but the SL shield stacks up quickly in this fight (lots of Fury/MC stacks)
Shadowfury - Definitely necessary to stop Engineer Repairs and as part of the stun rotation in the P1-P2 transition (literally the worst when a shield drops 0.5 seconds before your Cataclysm lands on a big clump)
Soul Link - 20% reduction is sexy as hell for the whole fight cause there's a lot of damage. Sac Pact is weaker since there aren't really singular big hits to soak (furnace blast comes in every 6-10 seconds in P3). Dark Bargain weaker as well
Burning Rush - Get out of the bad, Unbound Will might remove the Firecaller debuff in P2 but its not worth 20% of your health.
Grimoire of Synergy - Lots of procs
Archimonde's Darkness - Demo doesn't need KJC
Cataclysm - Lots of adds need to die
Glyphs:
Glyph of Eternal Resolve - more reduction yes please, Blast comes far too frequently in P3 to not take this
Glyph of Dark Soul - DS for every Cata
Glyph of Siphon Life - LOTS of Corruptions out meaning quite a bit of healing, overhealing in many cases but definitely helpful in P3 when your healers are pooping their pants
Glyph of Demonic Circle (Optional) - Useful to take off a couple seconds from your teleport as getting mechanics over and over again happens. A lot. Swap with Siphon Life
Glyph of Life Tap (Optional) - Personal preference here. Allows you to Life Tap without worrying about being gibbed by the mechanics due to health consumption, but with proper planning and awareness of your timers you don't need this glyph. Just don't Life Tap right before a Blast or other mechanic. Plus your healers aren't likely to see the healing absorb debuff whereas they will see your health drop from a normal Life Tap. Potentially a trap glyph.
Glyph of Felguard (Required) - 100% necessary to flaunt all the sexy 2H weapons that my Felguard got over Dk's, Ret Pally's, Feral Druids, Warriors, etc.
Blast Furnace specific Weak Auras
General
You'll be spending a lot of time in Meta for this fight due to the number of adds up at all times. Lots of Fury and MC stacks rolling in from DoTs and Imps.
Don't be afraid to make a lot more use of CW over HoG during this encounter. You'll have plenty of Fury and your Corruptions will be refunding a lot of HoG/CW charges.
Demonic Circle, Gateway, and Leap have a lot of use/utility in this encounter so make use of them to improve your performance.
The first kills usually last 10+ minutes so make sure to use your 10min Doomguard 2x with your potion.
Phase 1
Pretty much just keep everything DoT'd and funnel MC Soul Fires into whichever priority target you have at the time. In the opener, its pretty easy to get 2xHoG plus a Cata and CW off on the Bellows/Feldspar/Guard/Engineer pile all within your 10 second trinkets making everything melt for that first Bellows. I set my DG on Feldspar since everything else dies so quickly. My guild pushes to P2 around the 2:15 mark so I make sure to use my second Cata quickly if possible so that it is off CD for when all the adds get pulled together and AoE'd down as that helps a lot along with all the CW procs you will get. Note: if the Engineer is dying to quickly (we like to let it throw a few bombs before killing it), just request a Dk to grip it out or a Hunter to distracting shot it out of the group during the opener. You don't really want to change what you're doing against the other 3 mobs as it'll mean they are up significantly longer.
Set your Demonic Circle near the Blast Door so you don't have to waste time running over to drop bombs. I usually set mine to the side of it so that I am in range and can explode it there, but I am nowhere near the front of the door and thus don't get Allahu Akbar'd by other people running bombs. Additionally I place my Demonic Gateway through the middle of the room (during the boss reset) so that the other side can very quickly get to us with all the adds during the transition to P2.
Phase 2
If you are going to be using Cata on the Primal Elementalists, make sure to precast it as the shields are coming down so that you don't waste any of the 20 seconds. We kill each one using 2 slags so the DPS window isn't actually tight at all (only needs to get to 50% on the first one obviously). Because of this, I've found that its far more important to keep the adds under control so my guild has me focusing on them with Cata - usually 3+ mobs.
Just make sure everything has full DoT's for the DF and HoG procs. My guild doesn't debuff all the Slag Elementals (we only use 2-3 unfortunately) as they come out meaning they are taking 99% (90%?) reduced damage the whole time, effectively never dying. I wouldn't waste too many globals here putting up full DoTs, but they do still give you fury and Wild Imps if Doom crits. If adds are generally under control and I am waiting for the shields to drop on the Primal Elemantalist, I usually do a round on them for the extra gains.
I set my Demonic Circle out of the group essentially in one of the corners for the fire debuff so I can easily teleport out. Since you're already out there, you won't have to deal with the headache of making sure no one is in range for the explosion, and everyone has to adjust around you. Demonic Gateway doesn't have much use in this phase besides moving from Primal 2 -> Primal 3, and I usually don't bother putting them down.
Phase 3
First thing to do here is finish off the Firecallers and the Security Guards. The shields can affect the boss and with how quickly Blast is coming at this point you don't want the Firecaller debuff forcing you to spread and doing additional damage. This phase is pretty much a kill once your guild gets there 2-3 times. Make sure to try to use Cataclysm on the Heart of the Mountain as well as some of the debuffed Slag Elementals. It is a waste in my opinion to Cataclysm the 99% reduction Slags to spread DoTs unless they are all clumped up and you can hit a significant number of them (6-8 minimum probably) and save a lot of globals. Don't spend too many globals putting DoTs on the Slag Elementals, since it is technically a single target encounter at that point, and you're only doing it for the resources. Depending on the length of your kill you'll likely get a second Doomguard so make sure to save your second potion if you don't use it in P2 and a Dark Soul for that.
Demonic Circle has limited use in this phase due to the pace at which you move around the room. I have found that you can drop it in the pile behind the boss and use it to teleport back if you have the Melt debuff (and the Melt hasn't already covered your portal). Gateway can be used at the beginning to aid the first couple people with dropping the Melt debuff as far in the corner of the room as possible. If I have the chance, I'll drop the portal from behind where the Bellows were spawning in P1 to the back of the room. Use Demonic Leap to quickly get back into the raid pile after dropping Melt. If you're fixated by a Slag (especially one that isn't debuffed and can't be killed), make sure to stand slightly out of the group so you don't cleave them down. Save your Health Tonic for this phase if possible since Blast + Slag cleave + dropping Melt (and taking a few ticks of it) can leave you very low or kill you. Don't be afraid to call for an external like Sac if they are available.