If you're interested in hem-onc, let me know if you have any questions about UAB via PM, since I'm pursuing PhD work with one of the Hem/Onc folks here. I also have a resident working in our lab that is in the current cycle for Hem/Onc fellowships. I can tell you anecdotally that as an FMG, he's been able to obtain interviews at MDAnderson, WashU, and a number of other excellent institutions, but not at others due to some programs not supporting H1B visas, which include the Hutch, DFCI, and MSK. Unfortunately, I don't have specific information regarding the history of residency graduates getting into Hem/Onc fellowships - I'd ask Dr. Heudebert those questions specifically.
UAB is also in the search for a new medicine chair, new Hem/Onc division director, AND new cancer center director (med chair and cancer center director due to retirement).
That said, from what I have heard, Mayo is fellowship-friendly, residency-unfriendly, and Baylor's IM is overrated (how much overrated above say the rest of your rank list, I don't know).