Besides the APA endorsed combined programs, there are a few combined programs I am aware of in the NYC area. Farleigh Dickinson, Pace U, and Kean University are the combined programs I am aware of that may not be accredited (FDU and Pace may be, I'm not sure). There are a few combined programs that I know for sure are accredited programs in NYC area - Yeshiva & Hofstra. SUNY Buffalo is an accredited and combined program, too.
In my opinion, you gain competency through experience. That means seeking out externships where you can learn different therapeutic techniques. You can gain didactic knowledge by reading. It doesn't matter whether you are in clinical or school psych - what matters is the type of experiences you receive. Many school psychs get most of their experiences within school settings - they therefore get poor supervision and few practical therapeutic opportunities (since most school psychs traditionally are, likewise, not trained in real therapy). Therefore, if you complete most prac experiences in schools, you will NOT be a competent psychologist.
However, by seeking outside experiences (in hospitals, clinics, etc.) you can gain the experiences and competencies you need to become a competent psychologist. I have completed 4 practicum placements outside of schools. I have accumulated over 2000 total hours / over 800 direct face to face - more than others I know in clinical and counseling psych - I feel this has been a necessity, so that I can gain the competencies that school settings can NOT provide.
I transferred from a masters program into phd. I did receive some "advanced standing". However, it was challenging. I completed 45 credits towards a masters before enrolling a phd program - and I was only willing to apply to phd programs in school psych that would take at least half of my transfer credits. That eliminated many of the elite school psych programs that I originally intended to apply to (i.e. UT-Austin, UC-Berkley, U Maryland, Penn State). However, I was able to apply to many strong programs, as they did accept at least some transfer credits (i.e. UW-Madison and UW-Milwaukee, Minnesota, U Kentucky, South Carolina, Teachers College/Columbia etc.). Be warned, though - I was only able to transfer 24 of the 45 credits I completed!
FYI...In the midwest area where I live, I have seen numerous LD centers and places of that sort, some of which I know are headed by a school psych. So you can get into that sort of thing for a career. Also, there are hospitals and the like that will hire "testing machines". Lastly, you would fit in perfectly if you are willing to be a "testing machine" in the schools --- In fact, there is little point of your doing a phd if you are happy doing assessment with children and adolescents - since most schools continue to use traditional "gatekeeper" assessment approaches.
I definitely knew that, but my issue is not whether I can practice, but whether I am being given the tools to practice privately with a doctorate in School Psych. The truth is that I would be perfectly happy focusing(almost) exclusively on testing, but I am unclear there is a market for that skill alone. I am working on answering that question now, and if a doctorate in School Psych becomes a viable option in my eyes, I would go in that direction; there are definitely more school psych programs that grant advanced standing.