There's a couple of other ways, of varying accessibility to the current cast.
The Mystic Eyes of Death Perception would obviously work just fine, assuming they could a) get Shiki over from Mifune City, b) somehow activate her eyes, because at this point she hasn't even entered her coma, and c) get Enkidu to stand still for the whole thing. Obviously, that's not happening.
A Death Rune would also do it. This is, amazingly, slightly more feasible, except that as good as Da Vinci is, Primordial Norse Runes are a little beyond her. Not happening.
The obvious way is to kill Kirei. However, as seen in this chapter, that's easier said than done, and it isn't a walk in the park even for Serenity due to Enkidu's Presence Detection.
The non-obvious way will be what Caster tries next, having observed just what happened. However, that's really quite enough from me, so feel free to theorise about how you would deal with Enkidu if you were a magical supergenius. (Edit: unlike most times, I'm honestly not fishing for ideas to pass off as my own, I actually do have an idea. When and how it gets implemented is a little more up in the air...)