B.C.
Totally not the question you are asking, but have you tried working with sign language? Our youngest is on the spectrum and was very speech delayed, we started him on the baby signing times videos and he picked signs up very quickly. Also we started him on the PECs system, which is Picture exchange system. Being able to communicate more helps so much. I also can totally sympathize with the afternoon napping, Alex has given up naps now, but before he did he would nap for 3 to 5 hours at a stretch. The longer naps would be when he would have had major melt downs.
The school district should be able to point you in a helpful direction.