Don't be so hard on yourself. It sounds like you are passionate about bhsc and are applying for all the right reasons (because of the people you want to work with there). Express that in the application, the real deep reasoning you want to be at McMaster.
Whatever you do, I would definitely not position yourself in the application as someone you are not. If you are authentically you in the application, and you dont get accepted then it wasn't meant for you. Don't compromise your own beliefs, personality, and dreams to try and fit a mold of what you think they want to hear.
Remember, they get hundreds if not thousands of applications to read through. There is likely a lot of people writing what they think they want to hear. Probably a lot sound the same. Try and standout by showing your love for the field, your dreams and aspirations, the work you plan on accomplishing, and the impact on the world you hope to make.
It is the non-average people who stand out. Be yourself. The fact that you are introverted is irrelevant. Most people are. I was when I started at Mac. And I ended up building this site and learned to be comfortable with who I am and associated myself with people who supported me for being me. Find those people, and avoid the fakers.
Some inspiration for you: