Junior at Non-Target with no real experience; cooked?

I'm a junior Finance and Accounting major at a non-target school, and through my first two summers I've had no real finance internships. I've worked throughout college and have leadership experience at my job, but outside of that, my resume is pretty weak.

I've been involved with my university's general finance organization and spent time in our virtual student-managed investment fund. This semester, I'm planning to apply to my uni's other fund, our school's endowment-backed student-managed investment fund. I think I have a solid chance of getting in, and my technicals are pretty strong at this point.

I realized relatively late that I wanted to pursue investment banking, so I know I'm behind students who already have IB/PE/finance internships. I've recently started taking recruiting much more seriously, especially networking, and I'm trying to make up ground.

I'm now recruiting for junior-summer roles. How cooked am I realistically? What would you prioritize from here to give myself the best chance of landing an IB internship? I'm completely open to boutiques and MM firms and mainly want to get my foot in the door.