Hi Matt,
It definitely seems like the Specialist degree (Ed.S) would be more in line with your goals than a Ph.D. The specialist degree is much less research focused than a Ph.D. The programs are typically two years of course work, with some work in the schools, followed by a one year internship. Most school psychologist working in the schools have the Ed.S. degree. Ph.Ds in school psych are spread across schools, private practice and universities.
As for attending a program that isn't NASP certified, I would probably advised against it. It's my understanding that while it isn't impossible to become licensed after attending a non-NASP program, it's certainly more difficult. NASP's website has a list of certification requirements by state that you may find useful: http://www.nasponline.org/certification/state_info_list.aspx
I think only you can decide whether or not it would be worth it to switch to school psych, being so close to your MFT licence. School psychologists do a lot of assessment and very little counseling. Of course, this varies by school district, but I think that therapy is typically left up to social workers and counselors. If you're willing to let go of that part of your training, as well as spend three more years in school, then it may be the right move for you.
Hope that helps