It sounds to me like engineering would be a perfect fit for you! But I think you should find out for yourself if an engineering curriculum will satisfy your "why" questions. I seriously doubt that you will find that it's just a "plug 'n chug" field.
The first year or two of engineering and physics majors are very similar, so you don't have to decide right away. I'd advise you to take that path and see which appeals to you.
Personally I think you get out of education what you put into it, and you can go as deep as you want into engineering -- there is no "don't go past this line" limit.