First,you do not have to use Inga in order to get sagaciity.Though it does make sense to use the most advanced shaman,any will do.
Second, your question will probbably not be officially answered, it's not the kind of thing they divulge.
Lastly suffice to say, those pieces that are most useful , that drop from shaman or invaders, are those that do so with less frequency.
If it were possible to get them faster it might benefit you, but not them.