1) The OP made no mention of wanting to do research after getting his medical degree. In which case, he would be primarily a clinician and his priority would thus be getting into the medical school of his choice which would be made more difficult by an engineering major.
2) If his main goal is to research nuclear imaging and medical instrumentation I think most MDs and MD/PhDs would advise him to pursue the PhD solely without toiling in medical school. I would arbitrarily assert that 95% of what he has to learn in medical school would not be pertinent to such an endeavor.
3) To address your remaining points, I point to my own decision to pursue a dual degree. I had always planned on doing cancer research and am currently working on what I hope to be a very significant addition to our knowledge of glioblastomas. But I also want to treat cancer patients as an oncologist. There is a clear and useful overlap between my goal as a clinician and a researcher. For the OP's case I see no such relation given the limited information he's provided about his goals. Do you? What I've gained from the post was that he wants to go to med school, but is entertaining the idea of nuclear engineering as a major because he's tired of other life science subjects, not because he wants to find a way to merge his education with his future medical training. He also wants to maintain a 3.8 gpa, which most would agree is more difficult in an engineering major. He then asks if this is a good idea. To which I responded with a resounding no.
And just so you know, I premised my original advice with "if you know you want to be a doctor." If the OP was unsure about what he wanted to do with the rest of his life, having an engineering degree is a nice thing to fall back on. But that's why I included that premise.
Too many people here are vilified for telling the truth, even when it's soft.
