Talent mismatch

Haven't posted in a bit, but recently I got rejected for an internship with JP Morgan (AM). The rejection came less than 24 hours after I had applied and written a cover letter and everything.

I will note that this was one of the first 5 positions I applied to this cycle and it kind-of left a bad taste in my mouth. I'm not going to say that I'm discouraged, but I feel like there's a problem with these internships because they are almost always designed for "penultimate year undergraduate students" whereas people in their final year or in their masters seeking to get in literally can't because they should be applying to different programs offered by the employer. 

So a question for the audience - how do you actually get your foot in through the door without the obvious networking answer? Should people with so-called "talent mismatches" (compared to penultimate year undergrads, I'm a final year grad with the SIE and mentioned the CFA I'll be taking next year) be applying to merely full-time positions?