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I don't think there will be a ton of difference between the schools. They are all solid schools with good brand names and none of these programs will magically give you the job you want. As I'm sure you've found out this year, most BBs are essentially done by the time school starts. So for any hope of BB you'll have to use networking and probably accelerated recruiting. And even for EB's or MM's, you'll most likely have to network although your previous IB experience is huge.

You come from a semi target so I'd continue to leverage that network for more experience. A spring or a summer analyst position will help. On top of that, Vandy has some sort of internship program for early admits and someone mentioned that CMC helps their students find internships so that might be worth looking into. As you mention, some programs start in the summer like Duke, so the benefit of that is you have grades going into fall recruiting, but then you either have a short internship or none at all. Personally, I'll take the summer analyst over the earlier start because if you play it right, you can wrap up recruiting by the time you walk on campus.

If I were you, I'd work on getting the best summer analyst position as possible. Ideally, you could get one at a bank you want to return to after the program but worst case, get an offer and then shop it during accelerated recruiting. At that point, you leverage the network from both your old and new school.

ETA: Although with a 3.1 GPA, you might benefit from a summer start and get that over 3.5 since some IB's have 3.5 GPA cutoffs. Not sure if you can get around that with networking but if you can't tell by now, networking will be huge especially coming from a unique background.