Welcome!!! My daughter is the same age and has a lot in common with your son. A few thoughts on your current situation. First regarding OT, it sounds like you are willing to work with him at home could you afford to private pay for maybe one OT session a month and set it up where the OT gives you stuff to work on that month and then you come back?

Second diets and supplements. Gluten and Casein free diets have a great reputation to be helpful with kids with these issues (many are soy free as well), it has been extremely helpful to us. Artificial Food Dyes and Corn Syrup are also really tough on kids with hyperactivity problems and honestly are bad for everyone so I would eliminate those from his diet for sure, even if you don't want to do a GFCF diet right now. Cod Liver Oil is a good relatively inexpensive omega 3 you just give them 1/2 - 1 t a day mixed with juice - they do make chewies and such but the dose is low and the cost is high. You may want to look into some form of B-12, ideally a nasal spray which you would need a prescription for or if you can't do that (it's very expensive) a sublingual like the B-12 lolipops. Most of the natural treatments for Autism also help kids with SPD so if you are interested in that I would suggest looking for a DAN (Defeat Autism Now) doctor in your area.