To what extent are the many studies of identical twins reared apart complicated by the fact their souls and karmic influences may differ?

This is a significant problem indeed, and you can see that because each of the siblings begins to create a separate path for the portion of the soul incarnated as one of the twins, there will be differing histories accumulating based on all their life experiences. Whether together or separate, they will begin to even have a joint experience influencing them to somewhat differing degrees the more they become their own person, so to speak, through the course of the lives lived. While their similarities will be apparent, there will be differing environmental influences all along the way because unless they are Siamese twins always present together, their lives will take many differing pathways, and even Siamese twins have times when their attentions are completely diverted into their own thoughts and experience where one might actually be asleep while another is carrying out some life function and experiencing something highly significant for it. So the same situation applies, they are in fact individuals despite the fact they are joined together. So any research done on identical twins has the potential of revealing common influences but will be confounded by the individual differences that will always begin and grow during the course of a lifetime.