He sounds very much like my DS9 - dx ADHD combined type w/expressive and receptive language processing disorder (although on one of his CLEF categories he scored age-equivalent 5 yrs ahead... go figure).
Anyway, I've always suspected he has a sensory integration issue, and that's the first thing that comes to mind when I read about your DS. Sensory issues can wreak havoc. We've been through countless sensory behaviors and tried every fidget/chew/etc product out there it seems. (Thankfully he no longer eats his pencils, lol). His current quirk is ripping paper "I rip the paper so I can think." I've resorted to covering his duo-tangs with packing tape so that he can't rip them, but he still rips his lined paper and worksheets.
I am also surprised that you were given stimulants for him... my ped specifically warned against them (my DS has also had tics). She suggested that if we try meds we start with Strattera (atomexetine - I think? - a non-stimulant).
Re your comment: "The problem is that it seems like every professional that I've talked with only wants to look for a specific thing." ...ditto!!! Omgosh... isn't it frustrating.
Anyway, best of luck