I know you mentioned the states, but I want to just throw in two canadian schools, specifically because you mentioned Medtner.
McGill's Ilya Poletaev has recorded a lot of Medtner and makes a lot of students study or research him, and Stéphane Lemelin I think also knows his music well.
And the Universite de Montreal, while not an amazing school, is where Paul Lewis teaches, who is recording the complete works of Medtner I believe. At least, he's recorded all the piano sonatas and is either done or close to finishing the chamber sonatas.
Both schools have some scholarships, but they are way cheaper than American schools and UdeM, especially, is not very competitive. Just a thought.