So it seems that AnimType applies to the weapon when unsheathed, otherwise it reverts to the WeaponType value to get the correct AnimationSet. In this case, Quarterstaffs isn't one of the default WeaponTypes, so it uses the 1H animation set. Not sure how to work around that without doing something wonky like making these a Sword WeaponType, to avoid the Staff deltamods and get ones relevant to the stats used.
Ideally AnimType should apply to the weapon when sheathed too, or we need another field to override which animation set to use.