I would definitely wait. While your MPH may cover some material, you may be surprised by some of the other sections. I work in Molecular Biology / Infectious Diseases research, but I really had to study for Psych/Soc and Chem/Phys. Studying 5 hours/day is a great goal, but some days you may want to go easier. Additionally, it's important to break up your studying. For example, I would set a timer, read for 45 minutes, play a video game for 15 minutes, and repeat the cycle.
I suggest getting some MCAT study books (any publisher, year since inclusion of Psych/Soc will be fine; I used the 2016 Kaplan books for a 515+ score on a 2020 exam) and buying the official AAMC question pack with several full length exams [I got this bundle and it was definitely worth it
AAMC MCAT Official Prep Online-Only Bundle | 1-Year Subscription ]. This will allow you to study content and quiz yourself. If you are feeling utterly burnt out, do a minimum of one question per day. I definitely had days where I did this.
On weekdays, I had a certain subjects assigned to each day of the week (and sometimes studied different things if I really wasn't feeling it), and set a goal for an amount of chapters (of the Kaplan book) to read depending on my aptitude for the content and the length of the chapter. For weekends, I did practice questions. Prior to my test date, I did full length exams on weekends to get used to the endurance required and see where I was. After the test, I would check my answers and make a note on my weaknesses to study them more.