Breaking into M&A from a non-target

I am writing today because I am trying to break into investment banking M&A. I did not have a summer analyst position & it is off cycle recruiting, but many middle market & regional firms are still hiring. I have a plan to apply to 100 banks (applied to 30 so far) in total - regional, boutiques, middle market, bulge - and want to know if I have a chance.

I came from a non-target school (but top 5 public school), and did well academically with a 3.7 and a degree in econ and minors in accounting/management. I had 6mo of internship experience at an investment management firm getting hands on experience - value chain analysis, industry & economic research, valuation models (mainly DCF & Comps), due diligence, and execution of long/short US equities strategies. While not 100% of the experience applies to M&A, there is quite a bit of overlap.

In addition, I had leadership experience through being the president of a finance club & am currently studying for my CFA level 1. I am thinking this puts me in a marketable position and shows I'm hungry.

Does anyone have advice or certain or methods they used to break in?Any out of the box, unconventional ways that succeeded? I know I can get an MBA and come back to banking, but really want to work in IB straight out of undergrad. I have talked to quite a few bankers about it, but want to hear from the WSO community.