How to use a locational advantage in IB recruiting?

I am looking for soph internships and there's a small boutique bank very close to where I grew up and currently attend school. Really hoping to use this locational advantage to recruit for a soph internship because I go to a non-target and previous soph interns have been mostly target (usually W, etc., but also other regional schools). Added context: my resume is decent independent of school name (fresh. fin. internship, finance club leadership, 4.0 GPA). When I say close I mean in the local town less than 5 min away. 

Despite living in the same town, no one I know has a connection to anyone there. It seems obvious to me that my proximity could offer some sort of advantage but I'm trying to figure out what that looks like. I spoke with a current intern there and he said the process was pretty formal and that most people there are busy and will probably just refer me to the formal process if I try to reach out independent of it. Ideally, I'd love to intern there during the school year and also summer but there's no official program for during the year and I'm pessimistic about them being the type of place to make exceptions for that. I'm going to do the standard networking before applications but I think I'm probably more impressive in person than on paper so I'd like to get in front of them, preferably before applications begin so I can actually make it to interviews. What are some options here? How can I leverage this proximity without stepping over the line? 

Any thoughts, feedback, or comments would be much appreciated. Thanks in advance!