@totalboffin: Is there a way with mecanim to change the current animation given a string? If so, you could sync a property like:
string CurrentAnimationName { get; set; }
[RFC]
void SetCurrentAnimationName(string currentAnimationName){ ... }
//When you determine what animation is the correct one
tno.Send("SetCurrentAnimationName", Target.AllSaved, "TheCorrectAnimationName");
//Somewhere else pseudo code
mecanim Set Current Animation to CurrentAnimationName
So to sum that up, just sync what animation your object is supposed to be in. Once you have the current animation, you should just be able to get mecanim to interpolate to the new animation thus having it synced over each client.
I also don't use mecanim so this is all theory.