Your background in engineering should be way less rigorous. All places I am familiar with, all the important theoretical knowledge, you get during your BSc. The MSc is for application, research experience, internships and some specialization.
Best bet would be to find a place where you actually have synergy from your BSc degree. Now in this case with it being neuroscience, that will not be easy. Once you have solid job experience, the nature of your BSc should be less of an issue.
Did your GPA suffer because you lacked the basic courses? Did you follow all the high level courses or did you do mostly undergrad courses as part of your grad degree? A minor can hardly cover for 4 years of education. Now I understand in the US in college you also catch up on basic education not gotten in high school, but that's also why you guys have a fourth year.
They probably would still consider you, as you on paper should know more than a BSc, but if they don't want a MSc in ChemE and they want someone who has experience, they may flag you as less than ideal.
Just hard to see in which cases the Neuroscience BSc-ChemE MSc would be an advantage over all the other options.
In most places ChemE is an excellent degree for employment, so I would really start worrying. There's a lot more to getting a job than just your degree.