MPH before medical school?

I'm aware this question comes up every few years, but my situation is a bit different, so I'd really appreciate some advice.

I'm currently completing my BS in Public Health. My long-term goal is to attend medical school, specialize in Emergency Medicine, and eventually apply to the CDC's Epidemic Intelligence Service (EIS).

I'm especially interested in the intersection of emergency medicine, disaster medicine, clinical epidemiology, and public health. Areas that interest me include trauma systems, resuscitation science, sepsis care, evidence-based clinical systems, and emergency preparedness. Through an undergraduate internship with a county health department, I've also developed a strong interest in communicable disease epidemiology.

My university offers a 4+1 MPH through a top-20 school of public health. Because I'm on a full-ride undergraduate scholarship, my first 9 graduate credits would also be covered, making the MPH a relatively affordable option.

One of the main reasons I'm considering completing the MPH before medical school is the opportunity to fully take advantage of research, practicum experiences, and networking. From what I've gathered, those opportunities can be more difficult to maximize in an integrated MD/MPH program because of the pace and structure of medical school. Another factor is that the medical school affiliated with the school of public health has historically admitted a number of students from its MPH program, although I know that isn't something to count on. As for timeline, it would take 1 additional year past undergrad to finish the MPH, and because I finish it in August, I would have a weird 10-month period between completion and when I matriculate; however, I would most likely work in public health during this period.

Given my career goals, would completing the standalone 4+1 MPH before medical school be the better path, or would it make more sense to wait and pursue an MD/MPH instead?

I'd especially appreciate hearing from anyone with experience in the EIS, emergency medicine, physician careers in public health, or MD/MPH admissions. I'd also be interested in hearing whether you felt a standalone MPH provided meaningful advantages over an integrated MD/MPH.