This is NOT something that you should worry about! I did CV screening for quite a period at my firm and you have a well rounded background that if "sold" in the right way it is a no-brainer to any of the prestigous Strategy Consultancy firms.
The MBA adds value to your CV despite its low ranking, because it takes away the risk for these firms, because a very smart person (medical doctor) is not yet a "business person". A few of the medicinal doctors (alternative backgrounds) that I have met during my consulting period decided to move after a short period back to a field that they were previously active in because consultancy was not for them (they under-estimated the business work). I think your investment in an MBA takes away this risk.
However, having said that you are right to always ensure the right message comes across. I have seen in my period at most of the prestigous M&A banks and Consultancies that candidates were not invited because they were not at the "target" schools. There are two ways that you can increase your chances for a person with your background.
1) Find other people with similar background (either medical doctor or better medical doctor + MBA) at the firms that you are interested in. Ask them for a quick chat via phone or a coffee. The benefits are two-fold for you. First, it gives you an opportunity to find out if consultancy is the right path for you by learning about their experiences and pros/cons of consultancy / specific firm vs. a career as doctor. Second, it gives you a way in to the firm. I am without doubt that people with same background will try to help each other to get into the firm. They will recommend your CV to the recruitment team.
2) In case you are not able to find or connect with anyone in step 1. Ensure that you reach out and have a phone call with the recruitment team ahead of sending your CV. Here you ensure your positive elements are highlighted and any concern (low ranked university) are taken away. This ensures your CV is highglighted and looked into in full detail (since you have reached out this recruiter is personally "invested" in your CV. Otherwise, it might that your CV is just one extra CV in a huge pile of CVs.
Hope this is helpful. Feel free to reach out if any further questions.