Shamgarr at the EJ forums was able to test out resistances against level 83 mobs - and the results were a bit disheartening. Basically, instead of the 83*5 coefficient that he had thought, it looks like level 83 bosses (at least Sapphiron and KT) have a value of 500.
This means it takes 500 resistance to have an average resist of 50%. And more importantly this means you need 334 FR to resist at least 30% of all damage every time.
For gearing for the Sarth3D fight, this makes things harder, but not impossible. Now a leatherworker will need to wear a couple of green pieces or crafted pieces or old badge loot. A non-leatherworker is going to have a harder time; they'll need to wear a bunch of pieces. But it should still be doable.
Basically, because I happened to be wearing more FR gear than I needed to I lucked out the other day. I had a 4% chance of potentially taking a lethal breath. Now, thanks to the variance in both the resistance and how much damage Sarth can do, this ends up being a fairly low probability; he has to do max damage on a breath and I have to only resist 20%. But it could have happened. If you're curious, you have a 10.8% chance to take a 20% resisted breath with the aforementioned 277 FR - and that's skating a bit close to thin ice.
I apologize if anyone used this strategy and wiped because of my mistake. Hopefully luck favored you and you were fine. :)
I've updated the previous posts to reflect this new info.
Keep in mind that there's no absolute way to make sure that even this is correct. If this strategy doesn't work for you you can always use cooldowns or the Ciderhelm method, or a DK.