I think that with TKD and karate you will get the benefits that you are seeking. Both of them are part of a very deep and beautiful culture. In addition they both will provide the mental toughness, aerobic workout and flexibility that you are looking for. I would say since TKD features high kicks it might offer more flexibility training. I know its not the answer that you wanted, but you should check out the dojos and see if the instructors ephasize what you are looking for.