My main point is that core clinical training across the spectrum of programs is much more similar than dissimilar, and you can find mentors in research and psychotherapy in most if not all places.
OK, for "serious" psychotherapy training, n=1 (Yale, right?). Others will chime in, of course, on the special virtues of their program RE psychotherapy training. So how many programs are equivalent to yours? My guess - a distinct minority, maybe counted on one hand? Two hands? Whatever...
But the reality is the vast majority of us are happy with basic exposure to psychotherapy and other therapy modalities that we get in 3rd and 4th year, not the immersion in any one area. You say you feel competent enough to hang your shingle as a psychotherapist after PGY 3 (it would be helpful to hear what psychotherapists with extensive extra training would make of your self assessment), but I am much more concerned with feeling competent to hang my generalist psychiatry shingle after 4 years, and most of the people I know feel the same way.
The things that MS4s say about what they want in a program, especially research opportunities, seems to fade away for most folks once they see what that life entails, what life in academic psychiatry means career-wise, etc. No path to research or basic psychotherapy training is closed to anyone in virtually any program if you have the initiative and desire to seek it out.
My point to applicants: when applying and interviewing, focus on the core training, the teaching, the breadth of that training, the balance of work / life issues, etc.