No, I think your approach to motives might be right! In fact I don't think motives should ever be something you solve. At best it should be a reward for catching the culprit as they tell you the reasons why they did it in an epic confession, as a reward for solving the crime mechanics wise.
Basically the "why" can never be truly proven, only assumed or revealed. You can't really solve what's going on in someone's brain after all.