Best Sophomore Internship to optimize prospects for MBB Undergrad Recruiting / where to find F500 Strategy Internships?

Some context: 

 - currently a rising sophomore at a semi target that gets ∼15-20 hires a year (think Notre Dame, Vandy, etc.);

- mechanical engineering 3.96 GPA; involvement and leadership in two consulting clubs on campus and a philanthropic student org

- (1) fresh spring remote search fund internship (2) fresh summer internship in FP&A finance at a pre-IPO tech company (3) have a part-time, remote fall analyst gig at a LMM investment bank lined up for the school year 

- Founder of a startup that raised 20k in non-dilutive funding

Given this profile, I was wondering what soph summer internships gives me the best shot at MBB recruiting. From my research thus far on WSO, it appears that in house strategy roles at a F500 are my best bet. However, I've tried to compile an initial list of companies that might offer this type of summer internship, particularly those don't exclude sophomores, and I've struggled to make any traction. Does anyone know a more efficient method than manually looking up each company and periodically checking their listings? I've seen a few people on LinkedIn from my school doing biz-ops or strategy at a F500 for their soph summer, so I've wrote down those companies, but I really don't know how to go about finding more. 

Another item to mention is that I have a few other options. Deloitte Discovery, and EY-Parthenon Emerging Leaders are both non-diversity programs I can apply too. Further, there's a boutique in my school's area (they're a pure strategy consultancy) that starts their recruiting timeline sophomore year. Their program is a two year process where you intern as a Summer Analyst both as a rising junior and senior. Incoming analyst make 100k, but since it's a no-name company, many students do year one of the program then withdraw and recruit for SA roles at more reputable consultancies. Right now, my hypothesis on the best internships to help my odds at MBB recruiting goes in the following order. 

Deloitte, EYP > F500 strategy > boutique SA role 

If anyone could confirm that my current though process regarding what to prioritize is correct I would greatly appreciate it! Also, if anyone knows a way to identify these F500 strategy internships. 

Thanks!