I don't recall ever seeing mood swings referenced as an ADHD symptom. If he is having anxiety reactions and he has sensory issues, seems like the last thing to look at is ADHD. The DSM guidelines say: "ADHD symptoms must not occur exclusively during the course of schizophrenia or another psychotic disorder and must not be better explained by another mental disorder, such as a depressive or bipolar disorder, anxiety disorder, dissociative disorder, personality disorder, or substance intoxication or withdrawal."
Also, you mention he gets more sleep on the weekends. That's concerning, because being tired can get many of the same behaviors. Ideally a child gets the same amount of sleep every night. Adults may be more cavalier and even teens (not usually a good thing,) but for kids lots of executive function abilities can quickly unravel without enough sleep.
Though, if you reread what you wrote, I think you know all of this already. If my DS was in a similar place, my first concern would be adequate sleep. Then I'd be taking notes about the full situation where he has meltdowns, especially the amount of visual and audio noise in the situation if I was suspecting sensory overload as a trigger for anxiety reactions.
