I expect that you will find a PhD program at an Ivy league school to be incompatible with your current job unless the head of your lab was hired by the department with your intended degree. Unless a lot has changed, those programs are more about apprenticeship than education. They are full time jobs in themselves, and you pay tuition on top of that. Grants, scholarships, and loans may make it possible if you are good enough and were not born into the 1%.
That said, Mathematical Biology or Biostatistics departments might be your best choice. They are likely to have people that can teach you something without looking down on you too much for your history. In the dark ages, I worked for Dr. Carol Newton, in Chicago, trying to teach programming to biologists. Talk about teaching pigs to sing, the thought modes were completely incompatible. Musicians make much better programmers.
Recently, the big money in statistics was going to physicists as Wall Street tried to use statistical models. Those PhDs unfortunately don't include a lot of the practical knowledge a statistician needs when the assumptions are uncertain. The results may have made for some good openings for biostatistics folks.