The actual system does not give enough enough leeway to experiment many stratigies on a given monster. Moster parts not from the lord are too hard to get, there is no way to change parts and, even if these problems were solved, changing a team to try a new strategy that may or may not work would take too many runs, and that is considering that the desired parts would eventually be found. Given the situation, a way to choose a monster's parts during runs or before them would be awesome.
My idea is to make the collection of different monster parts more interisting. Players would collect them so they could later pay a price to choose a part from their collection and attach it to a monster. This increases the value of getting as many parts as possible from different monsters while making collection building more pleasurable. It also avoids that dreadful situation where this super valuable part spawned and there is no Ark monster available to take it, or Ark space to save it.