... that the discussion has been so much about the fact that there is violence as it has been about the perceived unnecessary detail and luridity of the descriptions of said violence. It's a position I only partially agree with, but that seems to be the idea.

Anyway, separating your question from its origin, you could easily envision fantasy stories without any overt violence whatsoever, simply by taking non-violent traditional story types and transposing them into fantasy settings.

Random examples pulled out of my ass:

Take a traditional detective story such as Sherlock Holmes, where much of the violence occurs before the story begins when there is even violence at all. Tell a story about a detective solving mysteries in a fantasy setting. As an actual example of this, you could take Neil Gaiman's A Study in Emerald, a Holmesian detective story set in an alternate London ruled by Lovecraftian horrors, a story told without violence.

Court procedurals are the same idea. The violence takes place before the story starts. Have a fantasy lawyer type character who tries to prove people innocent of crimes in a fantastic or medieval setting.

To borrow again from television, a show like House has no violence. Could easily be done in a fantasy settings.

Fantasy travelogue, humorously describing a trip through a made-up world.

Fantasy romance novel, taking a traditional romance story with adultery and passion and melodrama, setting it in a fantastic setting. Maybe the forbidden love between a human and an elf.

Essentially any traditional story type that doesn't use violence, of which there are many, could be transposed into fantasy with very little problem.