Moenghus may have counseled against it, but he may have wanted it to happen anyway, and structured his words to achieve this goal. If he started to set in motion the pieces of a holy war, then creating animosity between those two schools would be crucial.
As for the face thing, consider this:
The skin spy was assigned to Akka, and realized that replacing Geshrunni would be a great strategy, both to position itself well with the spires, and to get Akka's movements directly from Akka. It takes Geshrunni's face because it plans on replacing him.
The night the Skin Spy takes Geshrunni's face, Akka is instructed to leave Carythusal because of the coming Holy War. The skin spies already have an agent in the Spires, so they don't need a second, and they plan on having the current agent blame Akka for skinning Geshrunni's face. the Skin Spy trailing Akka follows Akka or is reassigned elsewhere, leaving a void in Geshrunni's place instead of skin spy replacement.
Rather than Geshrunni never being missed (and thus his body never being identified, because who would suspect that a person who was obviously alive was actually the dead man?), Geshrunni is immediately missed and his body is immediately identified. The skin spy in the spires, suggests that it was Akka, who has left so mysteriously, which has the delicious effect of making the Spires hate the Mandate even more, while also being yet another indirect way of discrediting the Mandate. The Mandate will presume the Consult is behind the war, and if the educated leaders of the Spires hate the Mandate for some new offense/brutality they will be even less inclined to entertain the Mandate's theories than the Spires usually are. To have the Spires discrediting the Mandate theories will only aid in the Great Names and other political factions also discrediting the Mandate theories, so it aids the Consult end goals in keeping the Spires irate with the Mandate.
To sum up, The face cutting is a tactic that is used when full replacement happens, so that no one will identify the body (how could someone be dead and alive simultaneously), but in this particular instance, the face was cut off and almost immediately thereafter the skin spy was reassigned, so the replacement was never made. But this was acceptable because it was possible to control the blame for the crime in a way that was advantageous to the Consult.