I have a PhD in Engineering Physics, which is the best of both worlds in physics and engineering. The curriculum has the theoretical physics classwork, literature search, and research of traditional pure physics programs but also applies the theory to an engineering research problem (in my case, quantum optoelectronics for free-space laser communications). That might be a great option. The degree is seen as more applied than a theoretical physics PhD by employers, and gives you the choice of pursuing an academic research/teaching or an industrial applied research and development career. I did undergraduate work in electrical engineering and mathematics, then the engineering physics later on, employed in the aerospace industry doing R&D of spacecraft navigation systems.