Good post, your a smart man.
Just to my knowledge I have never once ever seen or even heard of anybody getting hurt doing any sort of overhead lifting.
Ofcourse, the best thing to do to become a better pitcher, is actually pitch and become better on a mound. There's no dispute to any of that.
Ofcourse good nutrition is going to help you become healthy. Is this helpful for a pitcher? CERTAINLY. Just based on energy levels alone, it's important to become healthy. We've all had days when we're at work, or in the bullpen before a game and we feel a little tired. Just to have your body become more efficient and feeling good is a huge help for any pitcher.
Does swimming directly help you become a better pitcher? No. It helps you become a better swimmer. But I do believe that it can help you indirectly. When you combine things like swimming, yoga, a weight training program, nutrition, weighted ball throwing, it will certainly help me become a better pitcher. Ofcourse maintaning a strong throwing program with side sessions is vital, but that's not a problem.