Transferring Junior Year for Recruitment / Career Placement

I'm currently a sophomore at a state university looking to transfer to a target school for strong recruitment in investment banking, private equity, hedge funds, consulting, etc. Assuming I'm accepted, I'm wondering if recruitment opportunities will be available to me as an entering junior. 

For careers like investment banking, recruitment typically occurs in the spring of sophomore year for internships the next summer. Would I have any access to these internships if I were to do it after my fourth year and graduate one semester late, or after my fourth year post-graduation?

For careers like consulting with later recruitment schedules, would I have access to internships with no experience or track record at the target school?

Would an off-cycle internship during the school year be available/beneficial and provide me with similar opportunities?

Would I have any chance of breaking into these industries without getting prestigious summer internships?

I would have to take out loans of around 30k/year to attend one of these target schools, compared to no cost for attending another non-target state school, and I'm wondering if it would be worth the additional cost given the risk of poor placement due to my academic background

Info: 

GPA: 3.94 (I plan on having a 3.96 this year and maintaining a 3.8+ at target school)

Majors: Economics, Political Science

No past notable exctracurriculars/internships due to no opportunities. I plan on joining clubs and seeking ECs if I attend. 

I plan on getting an MBA a few years after graduation