3 primary methods of killing the Angel of Death that I've identified.
1. Traditional Berserker-based melee tactics. Old news, we know how this works.
2. Malicious Blades. Yes, it's that good- I just tried it a couple runs ago. Chainsword and/or a piercing knife is required; it'll be a really long fight with the AoD's 10 armor otherwise. (shit, it might be a pretty long fight anyways) MMB will easily let you go toe-to-toe with him, and while it is scary to have the screen flash red after every hit, only losing 2HP per hit is nothing short of awesome.
3. Items. Piercing Chainsaw + ridiculously stacked anti-melee armor. Shielded Armor is probably the absolute best, since it won't take damage, but there are a few other options. The AoD's frighteningly strong melee abilities limit the armor pool substantially; going off of the wiki, here's what I think'll work:
*Ballistic Shield
*Shielded Armor
*(Duelist Armor)
*(Ballistic Vest)
The first 2 armors will give you at least as much protection as Malicious Blades, and while your offense will be a bit weaker (single attack/turn, and you DID grab Brute at some point, did you?), they should make you tough enough to slug it out. Duelist Armor and Ballistic Vest offer much weaker melee resists, and they honestly probably aren't enough.
Hatred Skull sounds like a rather dodgy option, actually. No corpses from the Lost Souls, and a good chance of not getting many Demon corpses (do corpses actually stack?). Course, I'm salting those words now; I'd wager some loony like Tormuse is gearing up to get Longinus Diamond in exactly that fashion.
Yeah, I wouldn't say that the Unholy Cathedral forces aspiring Conquerers into melee builds, but the situation there does everything but forcing melee consideration. Planning ahead and getting lucky is the only real way to do it without a melee-based build. ....well, you really only need Berserker, trait-wise.