Canadian at Western University, Non-Ivey. Medical science background. How do I get my foot in the door?

So I'm a student at Western University, not in Ivey. I'm studying medical sciences and plan on going to med school. However, I'm also really interested in consulting and want to keep that path open, so I'm actively recruiting for a summer internship.

Without the Ivey name, I'm having a lot of trouble even trying to apply. Many companies only have applications open to Ivey students (such as EY Advisory, which I wouldn't mind working at). My GPA is okay (3.94/4.0, 90.1% average), I have decent extracurriculars and even some experience with healthcare technology implementation consulting.

I have two questions:
1) How do I get recruiters to look at my resume and cover letter? (broad, I know)

2) I have some chats lined up with people from Deloitte, BCG, and McKinsey, who I contacted through various alumni networks and LinkedIn. I plan on preparing a lot for the chats and asking meaningful questions. But I don't understand how I convert these talks to recruiters looking at my application. How do I direct the conversation in an organic way?