If you are mainly interested in an MD/PhD in Bioengineering / Biotechnology, why are you so committed towards staying in neuroscience/physiology? The degree you choose to study in undergrad will not pigeon hole you to the graduate school department you pick in for the PhD component of your training. There is also no benefit to completing two degrees vs. one degree when you apply to an MSTP program. Programs care that you did well in your degree program, scored well on the MCAT, and have extensive research experience (the area of which shouldn't matter, as long as you perform well and understand your science).
If I were you, I would think about majoring in Chemical Engineering, and focus your coursework on BME related topics. Any engineering degree will prepare you for graduate work in BME, since BME is a very nebulous field. For example, I was an electrical engineer in undergrad, am a BME MD/PhD student working for a faculty member in Mechanical Engineering who does tissue engineering and regenerative medicine research. Field doesn't matter. A BME undergraduate degree prepares you for a job in industry, that any traditional engineering degree can also prepare you for. A ChemE degree would also make it MUCH easier to get a job after graduation if your interests change and you no longer want to pursue medicine. Companies prefer to hire traditional engineering majors over BME, since they typically gain a deeper understanding in one specific engineering field as opposed to an overview of many different topics. Much of the biological aspects in BME can be self taught on the job or in lab.
Obtaining an engineering degree will make it much easier to complete the quantitative coursework required in any BME PhD program. You most likely will not gain the mathematics required to successsfully complete PhD level coursework in engineering if you have an undergraduate major in neuroscience/physiology. All graduate programs in engineering will require math through at least differential equations. It is also helpful to be familiar with quantitative techniques taught in an undergraduate engineering curriculum. You should not be concerned with techniques taught in a major / minor influencing the area of science you go into. Every lab you join will teach you how to become proficient with their specific techniques, which are often MUCH different than anything you would learn in an undergraduate lab course.
Essentially, if you want to pursue graduate training in BME, complete an undergraduate engineering degree (ME or ChemE are probably the best).