You may want to find out if your insurance covers SPD or Occupational Therapy for any reason. Our experience is that SPD is flagged by an OT evaluation - not the ped or neuropsych. There can be a long wait to receive services from a private OT facility and it is very expensive. Schools often have OT, but they do not tend to deal with sensory issues.
My daughter has been going to OT for a few months now. We waited a full year to be able to get her an appointment time after school. My husband and I aren't sure if she really has SPD or not, or if the therapy has any scientific basis, but she really likes going. My dd's issues are more vestibular/balance/sound related. 2 months ago she could not throw are catch a big ball (she is 8) and now she can play easy throw and catch games with us without dropping the ball. So even if I think its voodoo science, I see it working.
Good luck! It sounds like eventually getting your dc's diet more varied is a good goal!