If you can convince Tuck that you really want to go there (i.e. write an effective Why Tuck essay, spend the time to go visit the school and interview on campus) I think your chances are VERY good, even in a competitive round. I don't think they would pass on a highly qualified candidate that can help bring diversity to their campus who has shown demonstrated interest in the school. Tuck tends to take older/more experienced candidates, but I believe they would make an exception in your case.
Question for you: Why are you intent on applying this late? Why don't you apply next year. You could apply to Tuck through the Consortium (
www.cgsm.org) and be eligible for a full scholarship to Tuck if it is your dream school.
With your credentials you are also a top candidate at Stanford, Harvard (maybe you don't want to double up?) and Wharton as well.
Whatever you choose to do, put the effort in to write great (i.e. insightful, thoughtful, "real"/personal) essays and you should do well!
Hope that helps.