Publication can help, no doubt. If you combine publication with a higher LSAT score, you'd probably be looking at a whole new set of schools. Depends on what you're looking for; depends on what you want to do with a law degree. I think most people would recommend that you wait til next year... study and retake the LSAT... co-author the prestigious paper... and then go to LS. THE Ohio State University my ass. WTF. Those OSU people and their THE.
Seems like a risk to retake the LSAT. You may not do a lot better than you did the first time. And unless you do a lot better, I don't think it would help all that much. If you like Case, then you should go to Case now. No point in making yourself a better law school applicant if you're in at a school that you'd be happy going to.