Not sure if any of this helps you, but we went through an OT eval about 6 months ago when our DS was 3. I was convinced he has SPD, but the OT said he is "sensory sensitive" but does not have SPD or any other diagnosis. This is a child who has hated water since day 1, still screams when taking a bath, and has a whole other host of sensory experience sensitivities. Some of his reactions are more from emotional overexiteability than sensory, but they blend so it's hard to know why he's having a meltdown. We did the ASD eval with pediatrician and then saw a child psychiatrist, who echoed the same findings as the other two, does not have SPD and is not qualify as ASD. She actually said, "He's a genius in a 3 year old's body, it's hard for him."

In regard to worrying about public school evaluations, I did them myself, had 2E kids in many classrooms and I just differentiated like all Special Ed teachers do. I would have NEVER fudged numbers, there is an integrity to those tests and the people using them. The school psychologists are trained professionals, often times they come from other professional environments like private practice.
We are trying to decide to go public or private for evals, and the main upside that I can see for going with the public school system, is that a principal is more likely to hear what the school psych has to say rather than believe what a piece of paper says from a private eval from someone they don't know. The schools usually use the Special Ed teacher for the acadmice assessment and the school psych for the cognitive. They aren't perfect but can be very informative.
I hope whatever way you go, you find solutions and hope for your child. : )