I've bashed my head against Curious EB for quite a bit, and I'm starting to wonder if it's even possible. At the very least, none of my strategies seem to be working.
I first tried the same Paladin build that cleared regular EB so easily. That build can consistently get the boss to about 350-odd HP (and tears through Balder easily), but always runs out of steam at that point, mostly thanks to Corrupting Aura blowing all of my piety, preventing me from taking Cleansings or Protections. Even if I could take them (I had a run with 100 piety and Antitheist's Collar at Cocyteon for some refills) they don't do me much good because of how my stats get lowered.
The other build I've been trying is the Orc Rogue of Jehora -> Dracul, trying to maximise life steal, but even with 5 life steal I could only get the boss to around 350 health, and this strategy is way less consistent due to the huge amount of scumming involved. The main problem I run into seems to be that % refills are pretty much worthless against this boss, because he lowers your bars by so much (this is mitigated in the normal version by all the free refills you have). The bottom line is that the boss lowers your stats so much that 500 health is basically the halfway point for killing him (especially with the 50% resist, which you can't strip earlier like you can with H).
In terms of other power builds I use, I can't see any of them actually standing a chance here since most of them don't really have the staying power that life steal or the Paladin provide. In particular, Heretic isn't the massive powerhouse it was for VGT, because you only have the standard 4 gods here.
I'm going to keep trying, but if I couldn't win a Paladin run with Platemail, level 10, AND Serpentine Shield, I don't see myself clearing this run.