FT MBA Associate Recruiting for final-year top JD/MBA w/o finance experience?

• I'm entering the final year of a JD/MBA at a school with top-10 programs in each, have spent each of my summers interning in legal-oriented positions, and do not have pre-grad school work experience.
• I have an offer from the law-firm I was at this past summer, which is well-respected, but not one of the super-prestigous firms.
• I enjoyed the M&A deals I worked on this past summer, but after seeing things first-hand I'd much rather work on them in a finance-oriented capacity.
• I have a good amount of leadership experience from journals/extracurriculars at the law school.
• I have never recruited for banking in the past, whether in undergrad or grad school.

My questions are:
1) Do I have reasonable shot at getting a FT offer from a BB in the current recruiting climate? What about at a boutique or MM? How good are these chances?
2) What do I need to be doing right now to get prepared? Give me instructions and I shall follow your advice.
3) I love my classes for this year, but they are not finance-oriented. Should I be switching up my schedule to "prove" my interest, and what should I be taking?
4) Anything else I've neglected to ask about that I should know?

Thanks in advance for the help. Look forward to hearing from you guys.