7.6m health boss (Sartharion) divided by 15 DPSers is roughly 500k damage per player. Then there's built-in threat reduction, and they have to go 10%-30% over your threat to pull aggro, and you end up where there's no way in hell anyone is pulling aggro off of you unless they taunt.

This isn't difficult math. There shouldn't be any threat issues at all.

Hell, there shouldn't be any bosses where threat is significant to this point, except possibly Malygos on 6-minute attempts.

In my Sarth set, with MotW, i have 42200 hp, 29% dodge, 31k armor and 212 fire resistance. What you described is normal tank set, and i see no reason to taunt off you since your threat and avoidance are roughly the same as any other tank (you still miss some gear, my stats in normal set are a bit higher). But I dont understand why you'd maintank Sartharion is such set?

Some guilds do things differently, and some guilds wanted reassurance more than anything.

I MT our Sarth (if you even define tanking Sarth as MT), and after all drakes are down, and all portals are gone, the Drake tank will taunt off me and I will immediately taunt off him. This prevents the case of a wipe due to bad avoidance string in addition to healer movement during the easy aspect of the fight (you probably need both cases to happen to die to sarth after all drakes are dead), and it (death after drakes are dead) has never happened to us.

Sorry I posted my normal stats >.<

in my polar gear, selfbuffed I am sitting at:

33089 armor
35.48% dodge
39.9k hp

I can switch out a few pieces of gear and get even higher (not needed w. our raid composition):
I can get up to:
32899 armor
32.95% dodge
42.2k hp

Having the drake tank taunt off you also lets you innervate and battle rez people, but for a little extra comfort on the home stretch. We then have me go afk on the side of sarth opposite the raid so that if the drake tank does get gibbed somehow, sarth turns away from the raid and breaths me.

I'm not really sure what the issue is. If you gimp yourself with Fire res it makes sense to have the Drake tank who is wearing full avoidance to taunt off you once the drakes are dead and the damage is mainly physical. Are you saying you don't want to do this and want to tank it till its dead? Threat gear is really the last thing you need to worry about here given how long a head start you get.

If you really want to tank it 100% you can not use fire resistance, I found it more trouble than its worth given that we don't get big breaths in 25 and 10 man breaths are much easier to manage. But the whole reason for you to be tanking him is to absorb the massive magical damage. Once that component is removed you're sat there in polar gear, and possibly fire res, with less avoidance than normal as a gimped tank. If your healers can't keep you up then theres no reason not to swap out, which leaves you free to tank adds and use your other abilities like innervate and combat res.

We have finally managed to get him/her (?) down in 25, and 10 both. I should say, that 10 man S3D is WAAAAYYYYY harder.

Anyway, as I am not even nearly high end geared, I had to resort to some tricks. I would like to share some of those with you.

1. The pull. In 25's this is a no issue, as you usually get a hunter missdirect you, but in 10's we had no hunter. As my hit rating was a whooping 52, some wipes were caused by overeager dps leaning on the dragon while i see "Miss, Miss, Dodge". Result, raid dies in a flaming torrent. Convince your dps not the hit the dragon after pulling. But don't worry, if they are not listening: the second time they pull aggro, and wipe the raid, will convince them anyways .
2. Without the twilight torment debuff you are more than capable of handling a fire elemtal, or two. The issue comes up mainly in 10's - at least for us - when my healer gets aggro from a newborn elemental. Now, the load on the drake and add tanks is pretty high as it is, so you can lessen it by taunting, and killing those buggers off. But under no circumstances let the enrage. They will get loads of bonus HP, and will deal a lot more dmg. This can be managed pretty easily though.
3. I had the Power Auras add-on set up to show me when the Twilight Torment debuff is active. Use any add-on you like, but be aware, that this is the single most important thing to know. If you are like me, and have to use some cooldowns to survive the big breaths - beyond the obvious finger corssing ofc - then you definitely would not want to waste any of those precious life saving cooldowns. Again, this is mostly relevant in 10s, where I did not had any priest, or paladin ready to save my hairy bear ass. Why is this so important, you may ask. It is not unusual for the dragon to breath before the debuff gets applied. So, the third drake arrives, Sart is taking a deep breath, and you still don't have to use a CD, because you know the debuff is not applied yet.
4. Have the drake tank taunt Sarth off you after the last drake is dead. The dragon really hits like a truck at this point, and again mainly with 10 man raid the load could be very well too much for the healers already overtaxed by healing through the twilight torment, and the endless add waves. You can then bless them with an Innervate - oh boy, have you seen a gratefull shaman - and by tanking the fire elementals spawning. They are a joke for you anyways, beeing in FR gear, and such.

Thats it. Please forgive my rumbling, and I seriously hope someone will find this useful.

Don't use cooldowns till twilight torment comes up. Chart of what FR and sta you need. I highly recommend going for 340 FR as it comes with a very small loss of stamina and a big gain in mitigation. How you get 340 varies with what professions you are. What cooldowns you need depends on your hp from that chart. Obviously you can just add the strength of a FR potion or of SI/Barkskin to your hp. Oh, and make sure you're not hitting one cooldown as soon as another one ends, wait till he's actually casting the breath. That greatly increases the odds of getting 2 breaths with one cooldown. If you can keep 4t7, it makes it a lot more likely to catch 2 breaths with barkskin up.

Even with fire res flask, you only reach 285 FR with that set. But it is enough.

With that fire res I would recommend 54k hp buffed before the pull (you can often survive full breaths without cooldowns, provided you get quick heals after). Also, if your healer gets separated from you and you take a 30k breath, 7.5k swing, 7.5k swing you look pretty dead to me. (While it is possible to heal him alone, I'd recommend 2 healers on the tank)

For that SI, time a glyphed frenzied regeneration near the end. You get some big hits on you and healing up 40~60k takes a bit of time (especially in 10-man with only 1 healer on you).
I find BS alone is enough in 25-man. I prefer using an indestructible potion when the 3rd drake lands (helps the healer more provided you can survive without the fire pot).

All stats needed depend on raid setup and skill. Lower DPS means you have to survive more heavy hits. If your DPS is up for it, a warrior can maintank sarth-25 (kill 2nd drake before vesperon's acolyte spawns AND sarth breaths; this can sometimes take a much longer time than normal).

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@Jerikho
You can also use BigWigs. It gives a loud ding and screen flash when the acolyte spawns.

Do people use Fire res because their DPS is slow? I can imagine if the fight lasted a lot longer fire res could come out on top but I don't really see the use of it for say 4-5 or less "killer" breaths.

It means I can tank it without a single external cooldown, so theres no requirements to ensure we've got the cooldowns in the group (especially in 10 man). The only thing you really give up for FR is stamina (compared to the full stamina builds (bracer enchant, flask, stamina patches, tiny amount of avoidance on head enchant)), and you have more effective health against the flame breaths that you were stacking stamina for in the first place.