I'm be no means at all an expert on barbarian, so hopefully someone will give you some more reasoned advice.
What i do notice is you seem to have quite a lot of all res/armor but very low life on hit/life steal. According to your armory at the time of writing you have 2.8% lifesteal (belt) and 2 items with about 600 LoH total ( ring/pants).
At your relatively low attack speed i would think that you are just not getting health returned fast enough.
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he has bloodthirst on passive, so it's closer to 6% life steal. Getting more than that with the Skorn he has is likely impossible without MASSIVE dps drop. It's hard to tell from your equipment alone, but +500 AR is probably not enough for MP10 ubers. (what is your character sheet AR?)
Your pants seem to be the best place to make up some eph. With no set bonus and one socket, you're probably better off replacing those with pants that have 2 sockets and AR. Gonna be expensive to increase your eph with the 11% life and 100 vit, but I think you can find them.
You might try dropping some of the rubies and switch to amythest too. It doesn't matter how much dps you dish if you can't take one hit.
Have you tried finding some CM WW wizards to do ubers with? Your setup is pretty good for damage output if you can get some stunlock going. That would probably be my best recommendation is to find a group
I have been checking out some Depth Diggers before (extra resists) and was figuring Inna's would be more of a damage boost (Berserked im close to 300k but the increased regen might be the main benifit).
Any idea on the comfortable EHP for ubers 10?
CM wizards are allways welcome of course
I won't feel like having completed the game before beeing able to solo MP10 bosses however (and the elusive paragon 100).
Inna's aren't going to help you because they won't even come close to replacing the stats on your blackthorns.
I'd start with replacing that wasted random roll (dex) on your unity ring with something useful like vit or AR, easy upgrade. Also one thing I do is switch the hellfire when in uber fights with a more defensive ring, I use a litany with an average damage roll which gives a nice median of defense and damage.
You could put an Amethyst in your helm when doing ubers and also use a different ring instead of your HFR. Maybe 1 with resists or other kind of EHP. Just for the ubers, and you can still switch your HFR back when they are about to die if u think u need the extra xp.