Coming from experience, UMichigan is very NOT open to switching into any engineering if you do not have an engineering degree and specifically apply to their engineering PhD in your MD/PhD application. They send your app to the engineering department for review too.
However, Penn is very open to switching, baring the part about clearly stating your reasons for switching, taking necessary pre-reqs, and/or showing the people in the BE department you have a qualifying background.
I'm talking about post-acceptance though. Pre-acceptance is probably a different strategy. It's best, in my opinion, to stick to the research area you know best while applying (for various reasons like being able to concretely talk about your research expertise/interests in your field rather than abstractly talking about research in a similar, but different field...it just comes off as stronger). Then after acceptance, do what you want and talk to directors about switching like I did.
This is not in the school's best interest beforehand (they want "what you see is what you get"), but it is in your best interest (in terms of getting any acceptance somewhere and hopefully more than one so that you can choose the one best for you). I mean ideally, everyone should only apply to programs that align best to you, but come on now, in reality, that's hard to tell before you go through the whole process. Some places that I thought were on the back of my list beforehand turned to be great fits, and others that seemed to be great fits beforehand, after interviews and learning more about the school/second look, turned out to be not so great. This is where I learned most about departmental regulations, university policies, MD/PhD relations and its fluidity/communication with multiple departments, etc...
The point most important to remember, however, you can still be in an engineering lab, but be in a different grad program, at least at Penn. Like I can be in neuroscience grad group, but be in a lab that does neural engineering with other engineering grad students. This is because Penn usually have PIs affiliated with multiple grad programs, and if they're not affiliated, Penn will be like, we'll get them affiliated! Who cares what your diploma says exactly, because at the PhD level, it's really your research and skills that matter, not some title. At UMich, universtiy regulations are more stringent though, and I think you have to be in the grad program that your PI is affiliated with and some engineering PIs are only affiliated with engineering. soooo that might be a problem.
So again, it's program specific, but in terms of a general, blanket approach, it's best to apply to a program that aligns with your background and then talk about switching after acceptance. It may be hard to figure out how open each specific program is beforehand, so that's why a single approach is easier. I did different strategies with different programs, and at least for me, it helped to do the above.