I am about to go on internship and I am from a School Psych program. While all programs vary, I think that a lot have basic things in common.
1. I think that the type of program you apply to and how competitive it is would have a large impact on the admissions process. I am from a pretty competitive school psych program. Not everybody in my cohort came in with research experience. In fact, one specific individual in my cohort came in with an undergraduate degree that was not psychology. If you can express a very good understanding of what school psychologists do as a profession and why you think that it would be a good career for you I think you might be okay (depending on other factors such as GPA, GRE scores, etc).
2. Whether a program will allow transfer credits from a masters program is highly variable. You would have to look at individual program websites or email the training director to find out what their policy is. Even if they do take credits from a masters degree, it is highly variable what would be transferred. My program seems to decide based on how likely it is that the courses are equivalent (based on the university you are coming from and the syllabus from the class). They may also require you to "check out", essentially proving that you know how to administer an assessment or take a test to show that you know the material well enough. That said, I haven't heard of any programs that only require 2 1/2 more years in order to obtain a doctoral degree. My program, as well as many others, require 5 years to complete if you come in with a bachelors degree. With a masters, it takes at least 4 additional years of training.
I suggest considering what you would like to do with the degree and why you are deciding to enter this field. I would highly recommend choosing a program that requires at least 60 hours of coursework (specialist level) instead of masters level. Some states will only let you work as a school psychologist if you have a specialist degree. This should entail 2 years of coursework plus a year-long internship.
The majority of people in public schools are specialist level school psychologists. This level of education is respected in the schools and is rarely seen as "less than" a doctoral degree. Unfortunately, these programs tend to offer less funding. A doctoral degree will take at least 2 years longer to complete, but is more likely to provide funding for students. A doctoral degree will allow you to practice in many other types of settings (mental health centers, hospitals, universities, private practice, etc) and you can become a licensed psychologist. You will not have these opportunities with a specialist level degree. This makes it very important to be sure that you would want to stay in the schools setting before entering a program. However, doctoral programs are significantly more competitive.
I would not suggest starting a masters level school psychology program with the plan of obtaining a doctoral degree in the future. This will likely lead to you spending 3-4 years in a program unnecessarily. Remember that you also have the option of applying to both types of programs!
Sorry this post was so long. Let me know if you have any questions! I would love to help you out.