Nontarget - 3.7 Major GPA - 2.9 Cumulative GPA due to mid-undergrad major change

I've been attempting to network with boutique firms in my area as well as out of state, and was hoping to gauge WSO's opinion on my particular situation. I go to a nontarget State School in MA (Ranked 60-65 nationally)

I started my undergrad studying Chemical Engineering due partly to slight family pressure and lack of direction. I had no idea what Investment Banking was at the time. I hated the material, the major, as well as the future job prospects. I studied this for 2 years and completed my sophomore year with a 2.35 GPA. After doing some research, I discovered a serious interest for investment banking, switched majors to managerial economics, and have since never given up. I've been studying hard in my coursework and have a 3.7 GPA, bringing my cumulative up to 2.8. I often imagine what my life would have been like had I discovered investment banking in high school, but it's water under the bridge.

I should mention that some old engineering classes got counted as major-requirements, and my GPA for all coursework since switching majors is 3.87

I am currently a Senior, and will be staying an extra semester to fulfill some leftover required coursework. I have since taken part in a boutique private equity internship as well as a financial advising internship. I was wondering what my prospects are if I keep networking. (how deep is the ditch I'm trying to get out of)

Additionally, I know grad schools look at improvement over one's college career, so what are my legitimate prospects at this moment in regards to top 20 MSF programs?

Thanks for the help.