It sounds like you would prefer a BFA in MT program and I truly understand and fortunately, you have that option!
So many of my D’s peers who were in the acting studios at Tisch are very talented in MT and have gone onto MT careers including Broadway.
My D was in the CAP21 (MT studio at the time) at Tisch, but if anyone had told me when she entered college that after 5 semesters she would switch to ETW studio for 3 semesters, I would have not believed it. She is VERY into music and is known as a singer. However, she had more voice and dance training before college than acting and liked a chance to concentrate on acting in ETW, plus there was some singing and dance in ETW and she took private voice, and she wrote her first original musical in ETW and starred in it there as a project. So, it might be hard for you to imagine this too as a MT person but that is just the nature of Tisch and there are MT type students in all the studios and some opportunities for training and performing in those areas. She was also in an a coed a cappella group all four years at Tisch and many of the members were from acting studios. Many of them have gone onto successful music and MT careers. Just a thought. But it may feel to you as a better fit to attend a BFA in MT program.
(by the way, I always thought of PHS and Strasberg as the two non-MT studios that offered the most MT of the Acting studios, and then ETW)