PhD who wants an MD

Hello! I’m aware I have a bit of a unique situation, so I appreciate any help that can be offered.

I am an American doctoral student (3rd year of PhD) who wants to go to medical school after my doctorate. I’ve gotten some pretty varied advice and my school’s premed advisor has been less than helpful.

My situation: My PhD will be in Immunology. My dissertation is (tentatively) discussing the efficacy of targeted drug systems using nanoparticles. I have three publications so far, all in either chemistry or biochemistry. My overall undergraduate (which I finished 3 years ago) GPA was 3.38, STEM GPA was 3.23; my undergrad GPA steadily increased and I performed better and better as I went. I have years of research experience, as well as both volunteer and shadowing hours. I have not yet taken the MCAT, but am consistently scoring 510-520 on full-length practice tests.

What I’ve been told: the premed advisor at my school has said my situation is dire. I will have to do significant work to have even a shot at getting accepted. He has also told me that my PhD will be irrelevant and won’t matter on my application, as medical schools will look at my undergraduate GPA and reject me there. I have been instructed to try and work on my undergrad GPA, and so I have continued to take 1-2 undergraduate STEM courses per semester for the past 3 semesters (all A’s and one B). My advisor also said I should consider a medical masters program after my PhD to have a better chance of being accepted.

My questions boil down to: is my advisor right? What else should I be doing? And what other things should I think of that I haven’t already? Surely I’m not the first person to ever do this, so I appreciate any help that can be offered!

Thanks in advance!