Since the Tufts' master's degree is directly within the department, that gives you an advantage. I too have been accepted into Chicago's MAPH program and in researching it, have found that some students had a bad experience, where their "department of interest" did not want to work with them. It would be important therefore to check with the Philosophy department at Chicago. Send them a professionally worded letter asking them :
1) How closely they are willing to work with students in the MAPH program, 2) If they have had good experience with this program/ what they think of it (I've heard that some of the faculty are disparaging of it), and 3) If many students who were in the MAPH program get accepted into the PhD program there afterwards or into other schools.
Compare these answers with what you know or can learn about Tuft's program.