Seeking advice for IB recruitment

Hey everyone, I need some advice on IB recruitment and will be thankful for any help the WSO community can give me. I graduated this past December with a B.S. in finance from a non-target and want to work in IB. Since I graduated I've spent my time applying for entry-level jobs, networking, and also doing a part-time internship where I'm writing deal overviews on M&A transactions in the healthcare sector. The catch is that I have only one year to work in the states before either heading back to my home country or getting sponsored for a H-1B visa as I am an international student. 

Recruiting for a full-time job has been pretty tough, having done 400+ applications, sending out 400+ emails, and receiving only a couple of interviews (made it to the third round for a job, but haven't heard back even after emailing them so I'm assuming that avenue is closed). Considering that the job market is getting worse and I only have a year to work, I feel like my time will be wasted applying for (or even doing) a full-time job, especially since it will be that much harder for me to break into IB from a non-IB role. I know I want to work in IB if and when I go back home and I think the best way to hit the ground running there is to get an internship or two while I'm here in the states. 

I'm shifting my strategy for networking for full-time jobs to networking for internships - I'm mostly targeting small, no-name investments banks as they will probably be my best shot. Apart from the internship I have right now, I've done two prior internships. In my first internship I worked for a software startup cold-calling angel investors and VC firms to raise equity funding. In my second internship I worked at a fund of funds, sorting through investment data and writing investment memos. I don't have any IB internships but I'm currently doing the Adventis FMC course to improve my modeling skills and building DCF models in my own time. 

What would be the best way for me to recruit for an IB internship this summer? I've made a list of firms and will start contacting them this week onwards. I also think calling a few of them instead of emailing may help show some initiative and hopefully put me in contact with their recruiters. Apart from IB firms, I'm also targeting small PE firms and search funds. What else can I do that will get me at minimum a phone call or an interview? Do you think there are any other ways I can improve my recruitment process or chances for an internship?

I appreciate any and all help you can give me. Thanks so much!