You have my utmost empathy. Your testing experience sounds like deja vu of my DD's experience with the WPPSI. We did use a private tester, who had problems with my daughter refusing to answer easy questions, hiding under the table, jumping up, paying attention, etcetc. She did score around 135 as well, which was an underestimate of her abilities. She did the WPPSI around age 5, entered regular K but with an IEP and pull-out services, was dx with ADHD at age 6 and Asperger's at age 8. Based on my experience, here are my 2 cents:
* DD is still in her regular grade. While her academics are definitely 1-2+ grades above universally, her organizational, executive function, frustration tolerance, flexibility, and social skills are not adequate to help her handle higher level work as it would be presented in a classroom at a higher grade.
* Our first 3 years of school were hell. Our district refused to acknowledge that she was 2E--she was totally stuck in the "special needs" box--and basically operated on the policy, "We'll give her academic accommodations when she behaves like a normal kid!" Obviously, that amounted to never giving her academic accommodation. I feel this was actively damaging.
* We move to a different school district. Our new district is by most measures a "worse" district. But they know what 2E is. Our home school has a special cluster program for kids with Asperger's, where the kids spend much of the day in a regular classroom but attend the program for social skills groups and things of that nature. This has been a godsend.
* Homeschooling would have been better than school when we were in a bad school situation. However, if DD had homeschooled and had an autism dx, I would absolutely ensure she was enrolled in a social skills group several times per week and also attended individual therapy. We also do other group activities: 4-H, adaptive gymnastics, and swimming--which are all fairly structured activities. But I think the professionally managed socials skills group is absolutely a must.
* Is there a solid ADHD dx? It's a common comorbid condition with autism. But so is anxiety. DD has all 3 dx. She takes mediciation for ADHD and anxiety which is immensely helpful.